Thanks to @Wo3Dan, @john_drivenupthewall, and @filibis for your advice. I've come to a decision.
I'm not going to check the box. And it's not because I fear inappropriate earning of the badge (I still think self-bestowed solutions shouldn't count towards the badge), but because I thought about the particular thread in question in a different way.
This forum is primarily for users of SketchUp and other related products. Two categories exist that are tangential at best (this one, and the Corner Bar). As the thread I'm tempted so self-bestow as having a single reply as the "Solution" is in this category (Meta), it isn't really an answer to a SketchUp et al related problem. Furthermore, the "answer" doesn't, in my opinion, raise to the level of a "Solution" in that it was really a clarification of an obscure point about the operation of this forum - and easily discovered without looking for a thread marked as "Solved".
Have I cut a Gordian Knot? Perhaps. Now I'm just hoping that I earn that badge through "Solutions" marked by others before I face this situation again with the temptation to self-bestow a check in the "Solution" box!