Names and addresses of officers are supposed to be reported to our state because our PTO is a registered corporation.
I would ask them for the rationale behind the treasurer not being a district employee. There are some potentials for conflict of interest or possibility of theft. You might ask to have the district sit down with your officers and review the by-laws and the PTO's insurance guidelines. We have insurance that requires a monthly bank statement review and a yearly audit; it could be that you could assuage the district's concerns by pointing out the reviews you already have in place.
If my district asked for 10 years of records, I'd be happy to give them to the district to store, and get them out of my attic.
I passed on the records for the elementary school to the new treasurer, and she was planning to keep them, but the PTO is thinking to amend the by-laws that say we are supposed to keep certain records in a "secure place" in the school office -- we never did get that from the school -- and instead keep the crucial ones on-line. The thought is that (a) people can find them more easily and (b) the district takes care of backing up the on-line content (we have a "folder" on the school's web site).
The IRS requires that your Form 990s be "open for public inspection" for a certain number of years; if someone asked you for the 990 from two years ago, would you be able to provide it?