Ok.. whew.. smart money says walk away but.. here goes.
Distortion. First understand there are two different types involved, Perspective distortion and Optical distortion.
Perspective distortion depends on your distance from the subject. So yes, focal length comes into play.. sort of - a longer focal length will normally require you to stand further away from your subject, so it will impact perspective distortion in that way.
But even on a shorter focal length lens It is possible to compensate for this type of distortion by putting more distance between you and your subject, however this might also make it necessary for you to crop to get your desired FOV (field of view).
Optical distortion is a property of the lens itself. Wide angle lenses, for example, do have a tendency to show what is called barrel distortion. Straight lines will appear curved as a result, etc. Don't want to dive deep on this, just be aware that optical distortions are not the same as perspective distortion - but that both will impact the final results.
It's worth noting that the barrel distortion on a 35mm prime is more pronounced than it is on a 50mm - so it might require some additional software correction to compensate for - hence most peoples recommendation for the 50mm as opposed to the 35 for less distortion.
So, in essence both groups are correct. The sample pictures taken by various focal length lenses, for example - you see that the shorter focal lengths show much more perspective distortion because the photographer was changing his distance to the subject in order to keep his FOV (Field of view) the same. Closer distance, more distortion. You can compensate for this to a certain extent by getting further away, and if necessary cropping for desired FOV.
So, my recommendations:
Well for indoor shooting I actually prefer a fast zoom. My weapon of choice is a 28-75mm 2.8 from Tamron. On a crop sensor I'd probably look at something like a 17-50mm Sigma 2.8 with OS.
However, if your interested in primes, and shooting "candids" or "action" inside, yes, I'd go with the 50mm first. Less barrel distortion to deal with, and just keep in mind when possible back up and crop for desired FOV.
I will back up myself now, to give a proper amount of distance for the throwing of rotten vegetables... lol