If so - and the evidence does point to the authenticity of the famed quote - then here was certainly the defining moment in Melbourne's birth.
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Of course, Batman may have been attempting to make his mark after the event as the first settler rather than the area's other rather more zealous co-founder John Pascoe Fawkner.
Although Fawkner arrived in Port Phillip Bay six months after Batman, in October 1835, Fawkner brazenly squatted on land Batman had "bought" from the local Aborigines.
It may appear extraordinary that, with Van Diemen's Land hardly established in its own right, a group of pioneers should have wanted to seek land further afield.
While Hobart quickly grew comfortable with its role of colonial administration and convict superintendence, Launceston had meanwhile developed as a restless market town based on far-sighted men of commerce and industry, many of whom resented bureaucracy.
Indeed, The Examiner's first editor, Rev. John West, had demanded an end to the restrictive "convict stain" so that more free settlers could move in.
Both Batman (1801-1839) and Fawkner (1782-1869), sons of convicts, had become self-made men in Launceston.
Fawkner's father had been sentenced to 14 years' colonial transportation for receiving stolen goods.
Young John Pascoe, his mother and sister accompanied their father to the new settlement in Hobart in 1803.
After being deported for three years to NSW for helping convicts to escape in 1814, Fawkner junior returned to Tasmania in 1817 to work as a farmer, builder and baker, translator of French and amateur lawyer.
In 1824 he built the Cornwall Hotel and then, in 1829, established the Launceston Advertiser.
Fawkner lost the newspaper after using it to libel a local magistrate.
Batman was born in Parramatta, NSW, and voyaged to Van Diemen's Land in 1821.
He bought the rural property of Kingston, under Ben Lomond.
Not a keen farmer, Batman appeared to prefer to spend most of his time wandering around in the bush in pursuit of Aborigines or outlaws.
He won the confidence of local tribes and captured bushranger Matthew Brady in 1826, which won him extraordinary local popularity.
Claiming that there was not enough grazing land on the island, the restless Fawkner and Batman formed the 15-member Port Phillip Association at a meeting in the Cornwall Hotel in Cameron St (now the Batman-Fawkner Inn), the aim of which was to develop sheep country across Bass Strait.
Batman had already applied, in 1827, to Gen. Darling for permission to land a flock of sheep at Westernport but had been refused.
In the meantime, Batman married his convict bride, Eliza Thompson ("alias Callaghan"), at St John's Church, Launceston, on March 29, 1828.
Batman was to set out in the 30-tonne Rebecca on May 10, 1835, first establishing a base at Indented Head on May 29.
A week later he wrote back to the association: "We started this morning at 8am to find the natives ... we travelled over as good country as I have yet met with and, if possible, richer land, thickly timbered."
He continued: "The grass was mostly three or four feet high ... after some time I found eight chiefs among them who possessed the whole of the country near Port Phillip ... after a full explanation of what my object was, I purchased about 600,000 acres, more or less, and delivered over to them blankets, knives, looking-glasses, tomahawks, beads, scissors, flour, tea, etc., as payment for the land."
Batman also agreed to pay an annual rent of 200 pounds and sought and received the signature of the chiefs to such an action. (It has been subsequently suggested by some historians that the signatures were actually placed on the document by Batman himself.)
Batman then took a boat trip up the Yarra as far as it was navigable, writing: "I am glad to state about six miles up found the river all good water and very deep. This will be the place for a village."
Van Diemen's Land Governor George Arthur was keen on the new development, seeing it principally as a way of expanding his governorship even though the land, as yet unsettled by Europeans, was administered from NSW, where Governor Bourke declared Batman an intruder.
That did not stop Batman, on his return to Launceston, from walking into Fawkner's hotel and impulsively throwing up his arms and exclaiming: "Well, I am the greatest landowner in the world."
Fawkner did not take Batman's announcement well.
He sailed up the Tamar in the Enterprize, headed for the mainland - but as soon as the boat headed into the open strait, seasickness got the better of him and he was forced to be put off at George Town.
The exploration party continued and eventually landed at the very spot Batman had chosen to settle.
Even though Fawkner's party was warned off by Batman's associates, they took no notice, taking goods ashore from the ship and setting up accommodation.
Within a few days, Batman's surveyor John Helder Wedge arrived with a written order for Fawkner's party to quit, which was also ignored.
When Fawkner eventually got to Victoria and erected a dwelling on Batman's spot, the Port Phillip Association offered 20 pounds for Fawkner's interest, which he immediately accepted - and began operations on the other side of the river.
When Fawkner discovered that the original treaty with the Aboriginals was not recognised by the NSW government, or in other words that Batman had no right to ownership, Fawkner boldly moved back to Batman's land.
As more settlers arrived, Batman appealed for official recognition of the area. Former Tasmanian Attorney-General J.T. Gellibrand arrived in 1836 and noted that there were "at least a dozen" residences on the Yarra's banks.
By September 1836 that coveted official recognition was received.
When the first land was offered for sale in 1837, Batman bought the corners of William and Flinders streets and William and Collins streets for 135 pounds.
After recovering from his illness, Fawkner returned to Launceston to set his affairs in order so as to leave for permanent settlement across the Strait.
On arrival in September, Fawkner set about similar careers to those which he had had in Launceston, publican and newspaper owner, establishing the Melbourne Advertiser and Port Phillip Patriot.
He sought his place as a member of the establishment, becoming a major landowner and a Legislative Council member.
On his death in 1869, Fawkner was mourned as Melbourne's founder.
Batman's life was not so fortunate.
His only child drowned in the Yarra, and Batman suffered painfully before his early death from syphilis.
After his death, his wife Eliza had her cottage taken from her by the Victorian colonial government.
As for who earns the right to call themselves the true founder of the metropolis of Melbourne, there is, as The Weekly Courier of October 25, 1934, said "clearly much scope for difference of opinion as to which is entitled to credit for first action designed to lead to settlement in Victoria."
Marking Melbourne's centenary in a special edition, The Weekly Courier continued: "Batman and Fawkner were both adventurous, enterprising and resourceful."
It then conceded that "Batman's claims are clearly superior to those of Fawkner ... the original pioneering work on the Yarra banks was accomplished by him (Batman).
"All Fawkner's bluster and venom could not alter this fact, nor could he deprive that romantic figure of the honour of having chosen `the site for a village'," the paper said.
On that site Melbourne stands today, a monument to the judgment and long vision of John Batman.