In a yes/no question, a student gives the right answer and an unnecessary but wrong explanation. How to grade?
You asked for a yes/no answer (which, as you've discovered, has its disadvantages) and got one plus some other stuff. You should grade the yes/no answer and ignore the other stuff. If you like, you could add a note like "You got lucky! This is actually because..."

The whole point of yes/no or MC questions is that you grade only the answer, and assume that type-1 and type-2 errors cancel out or are normalized out. That paradigm doesn't work if you don't uniformly ignore everything other than the answer. 

More concretely: other students likely got this question right using the same incorrect reasoning, but didn't write their reasoning down. There is no way to identify these students; so, you need to make sure they get the same score as this student.