i had firemouths and convicts together no problems, so i dunno where you heard this from, it all depends on spp and tank size though, if you try to keep a firemouth and a convict in a 24" tank, you will have problems, if you keep the same combo in a 48" tank, you probably wont.
i found my firemouths to be more aggressive then my convicts, and they over came my convicts very time, i dont think this is normal, but it happens.