Thank you for all the thoughts.
I had the same thought about the “it should not cache any of its dynamically generated content” part of SiteGround’s answer so I asked for some clarification, about what that means in regards to the BPS Pro php error log file and they answered, “It is highly unlikely that that the SuperCacher tool would cache the file in question.”
Right now I have no new PHP errors in my PHP Error Log so I can’t do any more testing at this point. I will keep all of your thoughts in awareness though for future PHP errors. I have everything set up on my site as I did before (i.e. SuperCacher is fully enabled, and the 400 error line of code is removed from the CUSTOM CODE ERROR LOGGING AND TRACKING. If another PHP error comes up, I will first disable the Memcache in SiteGround’s SuperCacher and see if that makes any difference. I am also in communication with SiteGround and they’re happy to do some troubleshooting should the problem return.