They did not ground the plane. France and Italy (and some less relevant countries) denied usage of their airspace (though the french sorta-kinda dispute that?), then Evo Morales's plane chose to land in Austria instead of turning back. It could have chosen to land in any number of countries, or flown back. Portugal didn't even close airspace, merely denied landing permissions for a refueling stop - and while that's not entirely reasonable, it's at least comprehensible they didn't want to get involved in the Snowden drama.
Notably, it was in Evo Morales political interest to appear to be "sticking it to the man", so undoubtedly he had no problems with making the impact appear greater than it was. Not to mention his TV interview the very day before can be read as a kind of dare to do just this. Had he really been carrying Snowden with intent to protect him, he surely would not have played this brinkmanship game in the first place, but even if he did, he did not need to land where he did.
In other words, the US got played by Evo Morales who successfully demonstrated that the US can be pretty unreasonable at times. But the US did not take his plane hostage, not even via its allies; the situation is entirely unlike the Belarusian case at hand. Seriously: is being offensive to a diplomat that's knowingly playing a game of brinkmanship somehow equivalent to abducting a civilian plane?