As long as the agent used the lowest available booking class to quote from, the quotes should be accurate, so no, they're not able to make up the price...
Potential factors:
- Second agent possibly didn't use the lowest available space to quote with, maybe they didn't see it, maybe they assumed it wouldn't combine and they quoted, for example, an M fare when N would have worked.
- Availability for the second agent was limited. When they checked, someone else (or multiple someones), somewhere in the world was temporarily hogging all the lower inventory which meant it wasn't there for them to quote you in those few minutes. (ba.com can potentially quote lower prices as it has the ability to force some space in certain circumstances)
I believe a waiver of the offline service fee due to being unable to change online would have been allowed but things may have changed.