How is it that Indians have such a starkly different account of the Battle of the Hydaspes? Is there any evidence at all to back up that Alexander was defeated there?

I want to apologize to the mods in advance for my lack of formal sources in this answer. However the reality is that we're ultimately dealing with a question of a popular conspiracy theory, so you're not really going to have sources addressing what is just bad history.

As the other user has linked you to a great answer on the paucity of Indian resources on the subject, I won't add to it. Lets take that as answered. So we know that really the only real source of Alexander's time in India are Greek-Hellenic sources and later Roman authors drawing on them. So where does this idea of Alexander's defeat come from?

Well ultimately it is simply a historical conspiracy theory born out of modern day nationalism and revisionism exploiting that limited material. It ultimately argues that all claims of Alexandrian victory are "propaganda" and by looking at the events and citing the supposed lack of Indian interest and later references to Indian victories (such as Seleucus' supposed defeat to the Mauryans) as evidence that Alexander ultimately lost. It mostly relies on reinterpreting the "facts" (ie what is accepted as kernels of truth) from the Alexandrian sources and representing them in a different light. Its a form of revisionism, but one that rests on no direct evidence.

Where does the theory come from? Well it rests on a lattice of points. These are.

Alexander fought an extremely tough battle at the Hydaspes river. One where he came very close to defeat.
Alexander did not execute, displace, or punish Porus after his victory over him. This despite his satrap from Taxila being an enemy of Porus.
Alexander's troops soon after refused to march further and forced a mutiny on him. It is worth noting here that this factoid routinely confuses two distinct geographic entities due to the similarities in name. Alexander's battle was on the Hydaspes. His mutiny was on the Hyphasis. To us today the former is the Jhelum. The latter the Beas. Because they are confused though it is often presumed that Alexander's army mutinied at the same river he defeated Porus on.
During the mutiny Alexander's troops expressed concerns over the difficulty of facing the great empires in the Ganges and their armies of elephants, having struggled against Porus. This, as far as I know, is about the most accurate element of this lattice of fact, and is therefore cited the most aggressively as evidence that Alexander and his men lost to Porus and/or were terrified of Indian kingdoms.
Rather than turning back the way he came, Alexander instead turned south after his victory. This is presented as evidence that he was forced to head into an unfavorable direction.
The march across the Makran desert is presented either as a desperate retreat fleeing from Porus, or as a trumped claim to cover the "real" losses at Hydaspes. The conspiracy theory routinely ignores the entire Mallian campaign.
Alexander arrived in Persia soon after and died. Thus he must have really died from the shocking defeat at Hydaspes.

This is ultimately the dataset this theory is built on. It is largely a theory forged in 20th century, and gained popularity in the age of the internet. You will not find any mainstream historian or academic familiar with the source material or period espousing the theory. Unfortunately what is popularly accepted is not always historically sound or accurate, and the "Alexander lost at the Hydaspes" is a classic evidence of a viral conspiracy theory. It is not representative of mainstream academic thinking. As with most conspiracy theories, attempts to debunk are invariably criticized as motivated actions. So if you present evidence against it, you are dismissed as anti-Indian/Indophobic and/or dismissed as presenting biased or fake evidence. These conspiracy theories rely on mainstream historical theories on the complexities of archival material to distort what exactly is historical fact. Similarly building on the academic argument that examining the bias and "neutrality" of historical actors is important, these theories essentially make the claim that all the historical sources come from "pro Alexander" "biased" origins, and thus reframe it as a clash of a "neutral" argument against a biased historical one, one that was advancing a colonial or racist agenda of eurocentrism (again, appropriating known historical discourse to propagate a false narrative).

Ultimately though there is no actual evidence to the idea that Alexander lost, other than the fact that he "turned away." It is worth noting that internet conspiracy theories also often make the claim that Alexander actually lost at the Jaxartes river, because once again, he "turned away" there after defeating the Scythians. So he really must have "lost" since he would surely "never turn away." There's all sorts of assumptions and projections about Alexander and his motivations underlying these sorts of claims.