Sometimes you see something and wonder... were they serious? Could they honestly have been this ignorant, or is this intentional irony? Without any context it's hard to tell:
The answer of course is, yes, Nazi Germany did host the 1936 Summer Olympics. It's hard to imagine someone writing that placard without knowing, but then there are no limits to human stupidity.
Does hosting the games really encourage a regime to change? Almost certainly not. Would a boycott achieve anything positive? Almost certainly not.
Hosting the games may have been a propaganda backfire for Hitler, but it didn't stop him pursuing his agenda. I doubt a boycott would have done anything either. Boycotting the 2008 games probably wouldn't achieve anything more than insulting the Chinese leadership (do you think it would change their minds about anything?).
Basically the olympic games manage to be caught up in politics without having a serious effect on them.
No matter what happens, I think we'll end up watching the games as we would anyway. We might remark to each other how uncomfortable it made us feel to watch them given the country's politics. But that's about it.
In the modern world it feels like human rights abuse is just another spectator sport. The UN might send in some troops with easy-to-target blue helmets and no permission to fire back... but the full allied military don't mobilise for human rights, just oil. Any positive benefits for human rights are purely coincidental.