Did people really do their business in the halls of Versailes? Seems incredulous, so I wanted to know if it was true.
Short answer: No.
Long answer: Some people did, but it was not socially acceptable or the norm. It should be viewed in the same vein as someone peeing at the end of an alley in a modern city. It happens, yes, but doesn't mean that everyone in that city just pees in the street.
If you were a resident of Versailles you would have access to at minimum chamber pots, bourdaloues (designed for women who needed to pee) and public latrines. If you were a noble resident, you also likely had your own private closestool in your apartments, which was basically a chamber pot built into a seat--like a commode. These came in several styles, including independent chairs and seats built into walls, depending on the apartments. Madame du Barry had her own "chaise room," which was just for her toilet, at Versailles.
By 1789, there were also 9 flushing toilets at Versailles, though these were reserved for royalty and some exclusive favorites.
If you were a guest at Versailles, you would have likely used the public latrines or--depending on what era we're talking about--makeshift private "chaise rooms," which used screens and curtains. Chamber pots or closestools would have been in these.
Some people peed in public or semi-public areas, but these anecdotes are not particularly numerous and required contextual study. One anecdote recounts some servant boys who peed in the courtyard, near the window of a specific courtier, and kept doing it after he yelled at him. Another anecdote (from Liselotte!) recounts that they would kept seeing servants peeing in corners when they entered certain public rooms. Another anecdote recounts a man who gave up when the latrines were full and he absolutely had to go, so he peed in a stairwell.
So for these anecdotes, we have young servants who get yelled at (meaning it was not acceptable behavior) and later seem to do it deliberately; servants who probably couldn't leave their posts to go to the bathroom and made do but whose behavior was complained about (again, so it's not acceptable); and then a man who was about to pee his pants and did the palace equivalent of peeing in the bushes on the side of the road.
There's also an anecdote about the Louvre which is often trotted out, as it specifically brings up feces being in stairwells (since none of these these anecdotes, aside from this Louvre report from 1675, specifically claim people were pooping publicly at Versailles) but it bears noting that: 1) the report is derived from a single book by Anne Somerset, who does not source it so we have no idea where it came from or its authenticity at this point and 2) Somerset specifically says the report "may be exaggerated" because it specifically came from a man trying to get his closestool business a contract with the royal court. So it's not exactly a reliable source, considering that context.
Does this mean Versailles smelled like roses and there were never bathroom related issues? No.
Some people complained if their apartments were close to the latrines because of the smell. Mesdames complained about some of their favorites being lodged close to the latrines, for instance.
Sometimes, waste pipes carrying waste away from toilet facilities broke, which created a mess. There is one incident, and I want to say it happened at the Trianon chateau, where the waste pipes broke and seeped into the kitchens which had to be gutted and cleaned.
Sometimes servants tossed chamber pots outside windows into the courtyards, which they weren't supposed to do, but some servants still did it. Marie Antoinette was hit at least twice this way; after one of these incidents, a public notice at Versailles reminded readers that throwing chamber pots out windows was considered criminal, which means that this behavior (throwing waste out into public areas) was not considered socially acceptable.
Books and pop history media (like Supersizers Go) inflate these anecdotes about people urinating sometimes in public or waste issues gone awry and then create something entirely different out of them.
But "some people peed in public at Versailles and other people viewed this as gross" and "sometimes, waste pipes broke down and it didn't smell nice if you were near the latrines or cesspits" is different than the pop history notion of "The courtiers at Versailles were just peeing and pooping in the hallways and it was totally normal!! Oh that gross past!"
Now, different palaces had different facilities in different eras. Fontainebleau, for instance, was very much lacking on the toilet facility front in the late 17th/early 18th century. There's an absolutely hilarious letter by Liselotte where she complains to someone about being obliged to "hold her turds" at night because her apartments are on the side of the palace without interior closestools, and all she has available is a chamber pot in her room but she doesn't like to take a poop "into the air" without something underneath her. The only option if you were on that side of the palace was to go outside to some public latrines and do your business in front of others.
But even here, "People had to go to outdoor latrines at night if they were on a certain side of the palace and didn't want to use a chamber pot to poop" is still different than "people just pooped in hallways."