I really think that people are forgetting that there is nothing and no one more suspicious than a police person. A Police person in a missing person case basically live ‘Trust No One’. They won’t believe anything just because someone says so. Unless and until they have proof of their own then it’s just something they have been told.Just throwing this out there ...
It would absolutely be possible to make it look as if your computer has been accessed from home at a certain time, via remote software. This could be accessed via another computer somewhere else, or even a phone. Don't forget too, that some phones have dual sim card capabilities. It'd be easy to buy a burner phone SIM, and use that to log into remote software on your phone, before discarding it somewhere.