The simple answer is that it is true.

A more nuanced answer is that it may be true.

A somewhat speculative answer would be there is no way to know, barring new evidence.

There seems little reason to doubt that the major battles of the what I might call the canon (Granicus, Issus, Gaugamela, Jaxartes, Hydaspes) were Alexandrian victories. Same for his major sieges. While the primary sources are all in agreement, the issue is that they are not contemporary. Arrian claims to be working from contemporary sources, but since we don't have the source material, we can't be 100%.

The reason I raise the possibility for doubting the traditional narrative is that we are talking an immense period of time and space, in which huge swaths of it are glossed over by both ancient and modern sources. This is a campaign spanning 11 years and thousands of miles, involving tens, if not hundreds of thousands of soldiers, hundreds or thousands of cities, villages, and locations.

What follows is speculative, based only on a mix of research and reasonable extrapolation. To wit, given the scale of Alexander's campaign, we can speculate that our sources may not have documented all of the skirmishes and minor battles that Alexander was involved in. Armies usually march with cavalry outriders, scouts, etc. that may have been engaged with small bodies of opponents, and it may be that the Macedonians lost one of these skirmishes/minor battles.

I'm particularly thinking of Alexander's campaigns against the Sakae and Scythians, nomadic horse archers. He showed a great deal of adaptability and finesse in handling traditionally troublesome foes, that totally confounded many capable future commanders. Perhaps he gained that finesse through a few difficult skirmishes in which Macedonian outriders were soundly defeated and he adjusted his tactics to defeat them.

Again the above possibility is speculation. I have no, and am aware of no, evidence suggesting it. I am merely attempting to go a bit beyond a simple answer of "Truth." Edit: I know we have a rule against speculation, but I feel my speculation is more on the side of educating the questioner about the short-comings of our source material, and how that makes any answer about antiquity somewhat of a "In so far as we can tell..."

There is no reason to doubt the historical narrative that he won every major battle and siege, and that if we are considering only those battles we know about, then the assertion that he never lost a battle is true.

However, as the experience of David Glantz in researching the Red Army shows us, sometimes battles get lost to history. And given the lack of sources contemporary to Alexander, it may be that some of his battles are lost to history. But we have no way of knowing.

TL;DR: So far as we can tell, truth.

Sources:

Arrian, Campaigns of Alexander

Green, Peter, Alexander of Macedon