No one can actually point you to evidence, or reasoned argument for this, because it doesn't actually exist. The argument is made on assumptions, assertions, and shifting goalposts, often with a fair amount of the "No True Scotsman" argument thrown in.
But! What might be more useful is to go over some of the reasons people think this way, so that you can at least disambiguate what's going on when that argument presents itself.
Games where fiction affects play vs. not
First, it's important to note there is a key difference in defining something as an "RPG" because it:
The last one is pretty much the one thing tabletop RPGs have completely different than any other kind of game in existence, and as such, represents a unique medium of play. This makes it useful to recognize it is different than others for both design and experience, but that doesn't mean other types of games are bad or lesser games.
A lot of people are using this definition when they say other games "aren't real RPGs" even though they may not be able to articulate it as such.
What this means for Solo Games
Well, when you use that definition, a lot of solo games do not count - boardgames, "Choose Your Own Adventures", videogames, and even the solo random generated dungeon crawl typically doesn't count because there's no real rules to help a player to navigate which/how fictional events/choices should apply beyond the hard mechanical rules.
A core idea to multiplayer tabletop RPGs is this idea of "how does the group decide how the fiction influence play outcomes?" which is pretty much the idea of the Lumpley-Care Principle by Vincent Baker & Emily Care Boss. In multiplayer, it's really about figuring out who can say what and have authority to make it "real" as far as the game outcomes are concerned.
For solo play, on the other hand, there's just you. There has to be compelling procedures or concepts as a core part of play to make it more interesting than either:
"I win because I want to win, therefore I win." or,
"I don't win yet, until I want to win, then I win because I want to win."
(or lose because you want to lose, etc.)
In other words, there needs to be more creative pressure to make solo play something other than just the equivalent of daydreaming.
A few years back, there was a push for solo games by several designers and I know some came out of it, though the only one which I'm familiar with is Ben Lehman's Beloved. This game focuses on making an intense premise set up to force you to wrestle your own brain, intensely, as the point of play. Until I had seen this game, I also fell into the camp of "I haven't seen it, therefore it can't be done".
All in All
The arguments behind "you cannot have a solo rpg" boil down to either poor communication about what the game medium is you're talking about, or, simply the fact that most people haven't seen a 1 player tabletop rpg and just assume it is impossible.