I wouldn't know about turning a game around by talking, I don't even bother to communicate outside of VGS in a bad game since bm is typically flying already. The only other ways I've carried/turned Arena games around is getting fed/farmed or keeping better tabs on the minions then the enemy. If you aren't pushing the waves you aren't winning, I've witnessed so many games lost when the team that won had inferior K/D ratio because of lost waves. (Keep in mind a minion killing a minion does not result in a ticket but being blasted by a God will, meaning every wave is equal to a single God kill, minions vs minions results in no tickets and your own wave through a portal becomes a kills worth + depriving the enemy of a kills worth.)
I agree with you about being agressive - this is definitely key. I firmly think minions should be kept in check but it doesn't need to be done by all 5, past the first few minutes of the game 2 people should be more than enough and the rest should be actively zoning/harassing until an opening arises. Also, being defensive can work, there's just a difference between defensive and passive and too many people are passive thinking they're putting up any sort of defense. Being greedy is also a no no, you have to be smart about being aggressive.
Thankfully, it isn't actually that hard to be really aggressive and push the waves simultaneously. It's just, people tend to get pulled into 'Jungle' fights and if you don't have the wave advantage or at least in a stalemate you are gambling countless tickets, even if you break even in the team fight the advantage goes to the pushed wave.
I think defensive play is at its optimal if you have a crappy comp with no tank but a lot of damage(cc helps), they can clear camps and waves insanely fast early, thus they can get a foothold the enemy can't ignore and enough damage to mow down the tank early and proceed to snowball by rapid farm and countering initiations.
This is all opinion though, I just like talking about Arena strategies, since they are there just not as big or grand as Conquests. :P