[Marek_Tucan]

The AI doesn't cheat and uses exactly the same set of rules as we do - also it doesn't receive any special bonuses to morale or experience, if the suppression doesn't work then you may have encountered some die-hards or aren't suppressing enough (as often happens to me on advance).
As for the situation you describe, if your troops are suppressed, they don't shoot straight. Often it is better to break LOS (go to hiding or drop smoke) to be able to either have time to build up morale again or to atleast fire at the enmy at pointblank range when he comes through the smoke.
As for the opposite situation, if the enemy was in "pinned" status, then no wonder he opfired upon being fired. Sometimes he gets lucky, esp. if attacker is moving in the open... Just finished fighting one PBEM battle with a friend (the bugger got my HQ with his helicopter dessant) that involved close-combat fighting in a forest, plastered by arty from both sides - I was suppressed, he was suppressed, but still both sides were able to move somewhat, though greater proficiency of my Austrian Jäger units over his Militias was showing, still if I didn't want to get into pointblank slugfest, I fired everything available on targeted enemy unit (due to limited LOS using "Z" key alot) before moving in close with the assaulting squad and his units were usually too suppessed to return fire even at pointblank.
Try it out - machineguns Z-fired are a great suppressing asset, the same for say AA guns and their likes. Keep the enemy under fire up to the very last moment, preventing him to have a time off. Throw everything including kitchen sinks on the bugger and he'll break.