Is it true that grenade usage by aliens is not dependant on a situation, and just by chance depending on difficulty level? In other words, do aliens have a chance to throw a grenade instead of shoot?
As far as I've been able to tell, aliens that have grenades will always use them on purpose rather than at random:
When more than one XCom soldier is bunched up behind cover in the grenade's radius; the more soldiers bunched up, the likelier they get a shiny present.
When a single XCom soldier is in shooting range of multiple aliens, but all of them have lousy angles because of his or her cover; the first alien to move will lob a grenade and nuke the cover, after which the other two take clear shots at the now exposed (and probably soon to be dead) soldier.
Just like your soldiers, the aliens get one grenade each, and even on Easy mode the AI can and will choose to use them for maximum possible effect. No matter when one of them pulls out a grenade, you can be sure that you won't enjoy the outcome.
To expand upon the previous answer:
On Normal difficulty, I have only ever seen aliens use grenades when two or more of my units were close enough to be caught in the blast.
On CLassic difficulty, they will also use them against a single solider to destroy cover.
I have never seen this second behaviour on Normal. There may well be probabilities associated with both.