Well one of you is wrong? Or you're getting results from different places.
Measure again with another damp meter, if you still get 10% to 14% in the
area and beyond where you suspect dampness or where he's indicated there's a problem, then I'd be (very) suspicious.
Should he be correct, and you use his services, then make sure he dries
the area out and checks for any rot and corrosion. You wouldn't want him
sealing in the dampness!! Any woodwork rot is likely to be wet rot and requires replacement. If dry rot (unlikely) then this needs replacement and preferably
the area sterilised.
Usually sealing is done with one type of sealant, but perhaps he's bang up
to date with some type of current method ie with a two stage application?
Furthermore I'd defo get at least a second appraisal & quote/estimate.