Let's compare 2 scenarios:
-Player A has an ilvl of 346, and was 'carried' once through BWD, doing less than 10k the entire time. He died on every fight from avoidable damage.
-Player B has an ilvl of 359, and killed every boss except Nef. He knows the fights inside and out, and has never died to stupid mistakes
Going by the 'link achievement' stupidity, Player A would get an invite, and Player B would get turned down.
-Player A has done one run through of Bastion of Twilight, and is still learning all the fights.
-Player B has BoT on farm, has 8+ Cho'gall kills, but the character with the achievement is on another server.
Once again, Player A would get an invite, and Player B would get rejected. In fact, most 'must link achievement' pugs I see end up failing because of people who have only done 1 run or were carried before.
I actually had this happen during Wrath. I got into a ToC 'achievement only' run, and the RL was absolutely obsessed with having people who had the achievement. He was the only one who didn't link his achievement, and sure enough, after downing Anub'arak... (player) has earned the achievement [Trial of the Crusader]!
I put this dude on ignore right after I got my loot.