So the DS player Utinni 'd my Wedge Antilles which enhanced my (focused) Rogue Three

I knew where Wedge was captured so I play Rescue Mission which states:

"Rescue 1 captured card. If it is a unit, you may put it into play under its owner's control."

Now I wanted to put Wedge into play as an enhancement on Rogue Three again, but the DS player claimed I had to put him into play as a unit.

I claimed that Wedge's power to "You may play this card on a friendly Speeder or Fighter unit as an enhancement ..." could be selected regardless of whether I played Wedge by paying his cost or to use another card effect to put him into play.

Who's right here?

If I'm right that I can also use the "you may play as enhancement" if a card effect brings the card into play, this also makes it a legal move to put Wedge in play as an enhancement through the ability of the Falcon , right?

"Play" and "put into play" are distinct mechanics. Wedge's text doesn't apply to "put into play" effects. Both Recue Mission and Millenium Falcon are "put into play" effects, so you can't put him into play as an enhancement with them.

Your opponent was correct. Play is when you pay for the card. Put into play you do not pay. Wedges ability is a Play only ability. Play and Put into Play are both defined very well in the rules.

Thanks for the clarification.

Good thing I conceded since it was just a friendly game, then (I opted not to put Wedge into play due to the "may" qualifier and played him as an enhancement during my next deploy)