To justify this claim, they point to archaeological and documentary evidence that Temasek was a flourishing seaport in the 14th century.
The definition of a lot of history aside (for me, that requires a historical record starting in a year which ends in BC), while Temasek indeed was a port of some international note in the 14th century, the archaeological and documentary evidence may not support the claim that it was, as some venture, a major one. After all, the nature of international trade (even historically) was that even minor ports had walls and artefacts from all over their region - trade means that you don't have to be a major trading centre to have objects from all over the world.
For example, archaeologists have excavated Scythian graves from the Aymyrlyg complex in Tuva (Southern Siberia, in the middle of the steppes and quite far from the sea) and found grave goods including "woollen materials" (sic) from the Near East, Chinese mirrors and combs. Other Scythian tombs contain Byzantine gold and Greek pottery.
Furthermore, Temasek was attacked at the end of the 14th century and declined thereafter. In the early 16th century, the Portuguese writer Tomé Pires said of Sijmgapura that it "has a few Celate villages; it is nothing much" [Ed: Celates = (Orang Laut)]; in contrast, Malacca was a lot more important, and "whoever is lord of Malacca has his hand on the throat of Venice". It was then later possibly burnt down by the Portuguese in 1613, so from the 15th century to 1819, it indeed was a sleepy minor port.
Singapura may indeed have 7 centuries of history, but for 4 of them, it was indeed nothing much. As the Columbia Chronologies of Asian History and Culture summarises it:
The picture of a small port lying off the main trade route, at times tied to an empire and at times surviving on piracy, emerges from these disparate sources
Related: Balderdash: On The Insignificance of Temasek