I feel that the customer is responsible for the collected data at his end, and should protect the output file with appropriate permissions. The original O/S config+log files are not encrypted (unless the administrator uses an encrypted filesystem scheme), but rather by default O/S permissions.
But it is my responsibility to (at all cost) protect the customer's system info on my side, so ikegami's comment on securing the storage is important in my view. Being overly cautious is fine... and the suggestion about an alternative like a SSL webserver for uploads sounds good too.
When I get a bit of extra time, I'll do some tests to compare the straightforward RSA file encryption against the hybrid method, and post the results. I have a hunch that the time differences will be significant if the keys are generated upfront.