No, they said numerous times the heirloom would be for whatever specialization your loot was set for. Not whatever you were playing. You must have misunderstood them.
Also, you need to have your loot specialization (if it's different from current spec) set BEFORE Garrosh dies. For example: If you want a 2H Str axe, make sure you've set it to ret spec for loot, even if you're currently tanking/healing. Then switch loot specialization before bonus rolling fir something he normally drops.
Anecdotally, as I don't recall where I read this, weapons will drop over offhand for your first one. If there's multiple options for your spec (healers/Fury/Frost/Monks), you have a 50% chance of getting a 1H or 2H. Not sure about rogues, since daggers can be used as combat, but likely as well. Warriors/DK can force 2H by selecting Arms/Unholy or Blood, respectively. Monks, DW Frost, Fury warriors have to cross fingers on 1H.
...hrm, maybe I should get Flex Garrosh kills on my shaman for my monk....
IIRC, the stats on all 3 versions will converge at level 100, becoming closer together in strength as you level up.