That's actually my cheeky vision of you shaking your head.
I know and understand APA and follow it for titles and/or citations, as needed, but I have never used it for proper band names like A Tribe Called Quest, A Perfect Circle or A Silver Mt. Zion - to me the importance of the A in those names is indicated by their commonly used acronyms (ATCQ, APC, ASMZ.)
I do not do this with "The" bands, because somehow they are different. I can't, off the top of my head, think of any "The" band that has an acronym which incorporates the T. I'm sure examples exist, but not that I can immediately recall.
Either way: my house, my rules. Ergo, I am not wrong.