We have very old parquet flooring that needs to be redone. I believe it was last refinished somewhere between 10 to 20 years ago with oil-based finish. We have a contractor who says he can lightly sand the floors (so as not to wreck the parquet - I think he said "scuff-sand" or something like that), and then put water-based polyurethane on top. I remember hearing that you're not supposed to put water-based over oil-based finishes, but in this case, if part of the finish has been removed (although perhaps not all of it), and the old finish is really old at this point, would it be okay to put water-based polyurethane over? I just don't want to have him do the job and then have stuff chipping off.

Really no problem with doing that. I am always concerned about contamination of the finish over that long of a period, due to furniture polish overspray, cleaning solutions, and other things that may have occured over the last 20 years or so. A proper buffing and thorough cleaning should solve any of that, but remember that this recoat will do nothing for deep scratches, dents, gouges, and any other blemish that may be there now.