Armstrong as Gemini 13 Advocate And, Consequently, Apollo 11 Commander?

I read this bald statement, featuring no causality, in a picture caption in
a slick, soft-cover book done in 1994 for the 25th anniversary of the first
lunar landing.

Might anyone know "how it works"? I know that Armstrong backed up Apollo 8
as Commander; does his advocating Gemini 13 set up the situation by which he
obtained that seat?

By the way, found this group by a search regarding this question. Great
group, great discussions. Thanks much!