The problem is that there was a play in which Kelly Olynyk was involved in a tangle up with a player who happens to play for the same team as Glorious Senior Master Lord of Basketball Lebron James.
Lebron has some of the most irrational and moronic followers in the NBA today - not saying all of his fans meet this description of course, but when you are one of the top players in the league for years (e.g. Kobe) then you are always going to end up with a huge amount of mindless, brainless followers.
Unfortunately, Lebron's mindless, brainless fans also by default become mindless, brainless fans of whatever team Lebron happens to play for, and by default they then also become fans of whatever players he happens to play with.
So when there is a play where two guys get tied up, and a Lebron teammate gets injured, whatever player got involved in this on the opposite team is going to get labelled as dirty by a huge bunch of brainless, mindless Lebron fans who are too dense to think objectively and respond overly emotionally to the situation, because that's the only way they know how to respond.
If it was Avery Bradley who got tied up with Kyrie, and Kyrie got hurt, then the world would be calling Bradley a dirty player.
If Kelly Olynyk made that exact same play against Kevin Love back when Love was in Minnesota, when his team had no chance of making the playoffs, then the play would go completely unnoticed and nobody but the most die-hard emotional Minnesota fans would say a thing...and Olynyk wouldn't have a rep for being dirty.
It's nothing to do with who Olynyk is, and it's nothing to do with what he did. It's everything to do with the fact that he just happened to be involved in a play that led to a Lebron teammate getting injured, hence putting at risk Glorious Senior Master Lord of Basketball Lebron James's probablity of a successful championship run.