Legion of the Lost leadership

[bionic.beth]

The Legion of the Lost leadership says "your opponent chooses 1 non-Dazed character they control without the Incinerate special condition or the Immunity [Incinerate] superpower. The chosen character gains 1 Power and the Incinerate special condition."

If my opponent has no legal choice because all of their characters are either Dazed, immune, or currently Incinerated I would assume that part of the leadership does not trigger and they cannot choose a character to gain a Power, correct?

[Thoras]

Correct. It's only the chosen character that gains the power. If they can't choose one, there is no one to resolve the last portion of the rule against.