Tempting though it is, I would not go making special exceptions for widely-used user agent strings like this. You'll be back to square one in no time.

The other option sounds good. I don't know what the chatterbot hits to get the messages but I see no value at all in serving say FullPage Chat with a long cache time. Still cache it to avoid catastrophe but drop the cache duration down to 30 seconds or so. Hopefully that will go some way to solving it.