You can't tell that for sure.
Considering the amount of heat that Bioware/EA got for both of those incidents, then yeah, it's by far the most significant reason.
Compare it with the fact that numerous games/companies have released the first multiplayer DLC for games for free as well.
Now, can you name games/DLC that have been released because the user base funded it entirely through an unrelated in-game paid purchase?
Edit: For the record, I'm not denying that adding more unlockables helps their bottom line since they're accessible behind a paid option. However, the goodwill
(legitimate economic term) gained from the free DLC is far, far more valuable because of the *massive* heat they've generated from those two incidents (so much heat that they had to release a company statement defending the development process for the Prothean DLC, then go straight into releasing a patch for a
new ending for a 5-year old massive video game trilogy).
And if you've paid attention to the news, ME3 sold decently well (about 1.4mm) but not as well as they wanted. So yes, trying to rebuild that goodwill with the player base is far more significant than a couple bucks here and there.