That is correct. One cannot product change (PC) between personal and business AmEx cards. Within AmEx co-branded business AmEx cards, one cannot PC between different "families" (co-brands).
So, yes, it is basically apply for the Marriott
BONV°Y business AmEx card or not.
To me, the 35K Free Night Award (FNA) and 15 Elite Qualifying Nights (EQN) are worth the $125 annual fee.