Internal QA testing is probably more for glitches, testing new stuff, or visuals. Riot know what they want a champ to do and as long as it fits their design and does it as they plan that's all they are testing for.
PBE is for bugs and many builds in PBE are extreme and playtesters don't build properly. Riot don't truely know the full extent of how a champ will fair until releasing to the true playtesters. Us (and pros). We will abuse the champs, items or runes to the fullest extent and only then does this show where Riot need to make adjustments.
I remember when Sylas was announce so many people complained about his Ult, how OP it would be yet some of us just said "Wait, why is he healing for 500+ HP?" Maxing W allowed him to out heal any fight with his E shield. At level 9 when he'd have like 1300-1500 HP (based on items), he'd heal 500+ when below 40% HP, that's an entire 3rd of his HP with just a point and click which also dealt damage. This heal is now 260 (plus a better ratio), that's basically 50% less of a heal now and it exists like this because of how we (and pros) used him.