I can see one way in which this might be both true and proper. If each account was individually encrypted with keys that only the users had, what they're saying would be completely true. And I think it would be completely proper and even laudatory to run an email system that way. They could search individual accounts by having the users decrypt them, but they couldn't do a wholesale search of the entire email system. This is the way email should be!
A somewhat more likely approach would be that by policy, users are not allowed to keep email on the server. All email must be downloaded or deleted. No online folders, ridiculously small INBOX quotas, maybe a read-once policy where as soon as the mail is retrieved the server auto-deletes it. I can actually understand this being done; I've worked with corporate lawyers who would love to have the email system set up this way for the express purpose of defeating global searches. Anything can be twisted and used against you, so save nothing, leave no evidence. I certainly don't agree with that mindset, but I've worked with people who are like that.
Not that I think it actually is done either of those ways. I think it's far more likely that they're simply lying and refusing to comply. It's probably simply policy to refuse such blanket FOIA requests, and there's undoubtedly a clause buried in the FOIA itself that allows them to require that requests be specific and narrow. You know, in the way that searches of private individuals are supposed to be.