Supposedly, for Fahrenheit the band tried to go into a heavier direction since the first record didn't sell enough. So they tried to lure sweaty dudes to the shows. Hence Richie got to contribute more riffs.

However, The Hardest Part doesn't sound like Richie just tacked a heavy riff onto an already finished song. That songs riff is just three chords; I doubt you'd even get credit for that (especially since the progression in the verse uses these chords as well - they must've been in place before if the song was already around). And, as we know, both Richie and David got a writing credit for that track.