My wife & I had an agent that said that same thing on a recent award trip.
I couldn't believe it (my wife told me) so I told her to call back and talk to a different agent...so she did, and the agent didn't mention it at all.
Granted, this is me coming from the UA-side of things where there has never been an issue on changing flights or booking them. I've had quite a few issues on only a few award tickets on CO in the past few months...but luckily, this wasn't one of them - after we called another agent.
Our itinerary was 'somewhat' complicated, but that doesn't allow for a system that can't handle these simple requests. We had a SA flight connecting to a VS flight connecting to a UA flight on a one-way award and wanted to swap out the VS with a SA segment...this is where the agent said that 'it might cancel the whole thing out'.
It sounds like CO has upgraded their systems (from the previous poster), but ours worked out okay, but believe me - I was checking the PNR the entire time the agent was working on the ticket and for about 24 hours afterwards to ensure the transaction went accordingly.
-jeremy