What can they possibly be doing in the firmware or the ROM to break TLS (and other such authenticated key-exchange protocols)? The only thing I think of: Injecting a compromised https stack in to an app's classpath / ld_library_path. This may sound ambitious, but the Android modding community already uses such runtime swappers to great affect [1][2].
[0] https://news.ycombinator.com/item?id=9072424