Several years ago my parents decided to have their 150 year old house covered in vinyl siding because it needed to be painted nearly every year to look decent. Even though all the wood shingles had been replaced (some more than once) they just wouldn't hold either stain or paint for very long. I advised removing all of the old wood shingles and carefully inspecting for insect damage and rot before installing the siding, but the contractor said that he had checked out everything and it was fine. It turns out that all he did was walk around and stick a screwdriver up under the shingles in a few places.
There are now two places on the house that have massive termite damage. In some places, the ledger beams have completely disintegrated. These were 6"x8" beams and I removed part of one with a vacuum cleaner. It looks like the termites came up through a post under the porch and worked their way through the framing. If I had not added some framing to the porch a while ago I am sure that it would have collapsed. You would not believe the damage. I will post some pictures if I have a chance but there really isn't much to take a picture of, the wood is literally just sawdust and wood chips.
The house was inspected for termites about 3 years ago when an exterminator was called in to take care of an issue with mice. He didn't find anything. The issue is that they can be inside the wood with no external signs to speak of. You really need to drill into the beams to make sure that they are ok. This is a major issue with covering over old wood with vinyl and aluminum wrapping. You just can't see what is going on underneath.
Regardless of what type of siding you use, I would remove old wood underneath before installing it. I would use ground contact pressure treated wood for anything near the ground or foundation and I would douse other exposed wood with oil based copper naphthenate before covering it up. I also use pressure treated plywood for the first row of plywood on the outside.
Products like Azek and Hardy fiber board are great as they don't have this vulnerability, but you cant build the structure with these. While you have things opened up, make sure that the structure underneath is sound and well treated. I would never advise anyone to put vinyl on over old wood. I was against it before and my experience tells me that I was correct to be concerned.
I realize that this is not just an issue of how the siding was applied. I could have removed all the old wood and treated the new wood and still had a problem. Insects can be difficult to deal with even when you do everything right. I think removing old siding before replacement gives you a chance to do a proper inspection and treat the framing and this gives you the best chance of avoiding a major problem. This is even more important if insect damage is common where you live.
Needless to say I am a bit sensitized to hearing someone suggest putting vinyl over old wood and calling it a day.
LMHmedchem