Just have them staple another layer of plywood over your OSB subflooring. That is the recommended approach when a subfloor is questionable unless there is rot or damage to the subfloor, in which case just the damaged area needs to be repaired. Read this "sticky" on subfloors and underlayments.
http://www.hardwoodinstaller.com/hardwo ... .php?t=385
Quote:
Underlayments are not subfloors and subfloors are not underlayments. Underlayments can be safely removed; subfloors should never be removed EXCEPT for damage or remodeling and only by licensed, knowledgeable contractors. Underlayments always go on top of subfloors and are usually stapled but can be nailed, glued, screwed, etc.
Quote:
These subfloors should NOT be removed but overlayed with 1/2" CDX plywood that is well stapled (2" around perimeter and 6" oc.) or glued or screwed. In all cases, subfloors and underlayments are to be flat to within 3/16" in a 10' radius.
No need to remove the subfloors the way I see it. Just go over them. I do this ALL THE TIME. Good Luck!