That'd odd, because I'm pretty sure my heroic ToT achievements say that you can invite me to your raid and expect me to be able to, at least, handle those fights for which I have achievements. I'm pretty sure that if I had an achievement for full clear of normal SoO (which there may be no achievement for, as was the case in ToT... fortunately, the armory displays how many kills you have in each mode, which is a fine replacement for such an achievement), that would tell you that I can handle Flex raid. I'm pretty sure my Realm First Grand Crusader achievement tells you that I perform well enough to beat everyone else on a server to a no-wipe kill.
So, yeah, I'm pretty sure achievements do tend to say something about your performance. Either that, or they say that you have enough gold to buy your way into a run. Either way, there's nothing wrong with expecting decent performance from people with decent achievements. You can always kick them from the group if they aren't performing. Get this already.
And, as is always the case, a simple armory check of a player will generally tell you enough about them to know whether they're worth inviting or not. Also, as others have said, there's the gold proving grounds achievement.