Think of a record producer as the head or director of a team of creative individuals. It's all about people management and getting the creativity to flow in the right situations. I wouldn't consider a producer who just mixes, a producer. That's an engineer. Even though they don't always get a written credit for it, a huge part is arranging and helping the songwriting process. George Martin co-wrote tons of the Beatles stuff. Mark Ronson wrote a lot of Amy Winehouse's stuff on Back To Black.
Produce is an art.
People need to stop limiting art with titles. Some Rock producers do nothing, don't press on button, just tell people to redo their vocals or tell the engineer to pan the hats this way and the lead guit that way.
Others may be the lead singer/guitarist, and songwriter in the band and just step up to go the extra mile.
There's a million other scenarios between the two, same as any other genre.
And yes. Even some Rock is done over 2 tracked "beats" someone "produced" without ever being in the room like a Pop or Hip hop song. It's been done by Jewel, Kid Rock, Linkin Park, Limp Bizkit, Pink, AFI, White Stripes, Maroon 5, and I'm willing to make a bet from her sound, Katy Perry.
There shouldnt be a lot of difference between producers form Rock or Hip Hop.
Rock does however involved with more instruments and more channels than Hip Hop.