I am not a roofer but I have slept in one of those motels and I've lived under roofs for nearly 60 years. Means I probably won't have a good answer and I'll likely confuse the issue.
I have inexpensive, bubble-shapped plexiglass skylights. If I was going to re-roof, I would replace them because plexiglass cracks and does all manner of things that you might as well correct while you are there and the additional cost wouldn't be much.
Velux, on the other hand, is a great product with an equally great reputation. My expectation would be new flashing only and you'd be good to go. I would look at it much the same as new siding on your house....if you got new siding would you expect to have new windows and doors too?
Now the tricky part. The roofer that comes highly-recommended feels differently. I'd ask him why, in light Velux's assurance, would he really want to do the additional work:
If you say no, will it affect his warranty? Will he be doing anything that affects the water-tight nature of the skylight?Can't he assure a water-tight roof by doing the same good flashing job around the skylights that he does on the rest of the house?Were the (existing) skylights an add-on and may not fit exactly the same after he does a tear-off of your roof (if that's the case I'd side with the roofer immediately).
My suspicion is that the roofer is trying to cover his backside and not get into a situation where his good work and the good reputation you sought are called into question because of a leak from the skylights down the road. If he has been burned with similar problems in the past, you might expect him to stand firm on the need to replace what seems to be perfectly fine (but 11 years old) skylights and warranty the entire job.
Try this if the roofer stands on his claim they need to be replaced if he does the work:
Ask if he will do the skylights on a strictly cost-basis. Lets him protect his reputation and you are assured that the new ones are made an integral part of the job without spending more than absolutely necessary.Ask your General Contractor if he will write the job using the roofer as a sub and guarantee the work without replacing the skylights. My suspicion would be he won't want to.Consider getting another estimate from an equally-qualified roofer.
When everyone you ask points to a single source and says: "Go with him", you might have to honor what created that person's reputation and respect it or go back to your friends and ask who their second-favorite roofer is.