Is that really that clear?
I don't target the players! This "for each opponent" is the part that confuses me ... somehow the number of permanents that can be targetted isn't clear at the moment I declare the spell. What if there are 2 opponents but one has no permanents or all of his permanents are not targetable, am I allowed to radiate it?
It says target permanent, so when you play the spell, you have to declare it target(s).
If there are more than two players, your spell will have multiple targets (unless, as you well state, only one opponent has legal targets for Blatant Thievery).