I am doubting the security aspect, no system is 100% secure period (even if it is a MAC blessed personally by steve jobs)
The next best thing is to ask Sky for a specific time or day log of the usage or if you have monitoring in place would be to check that alongside the browsing history.
It is important to note that one log file is not enough to prove anything on the computer, it would have to be on the router or router level to dispute internet usage. I.e. wireless and ethernet would need to be monitored.