I remember reading of some public figure being exonerated for having adult theme images - not porn on his PC as it was later proven that he had not accessed the said sites.
Hard to know without detail, so no comment.
How can images appear on a PC without being downloaded?
Images, being just files, can "appear" on a PC through any of the multitude of means that a file can appear on a PC. And subject to directory write-privileges, they can be written to any location.
Can internet activity be spoofed?
Can't say "no", because like anything in computing, a computer will do what you tell it to.
But I would say very much unlikely given its not a useful attack vector to anyone.
The current trend being for phishing and pharming attacks.... which use other means to get a user to visit stuff.... but that's done elsewhere.
Plus Windows machines, and especially web browsers will leave very specific forensic trails. It would be quite a lot of hard work to accurately mimic those.
I never asked for that forensic document you offered in another post, and I'm not willing to either. Not because I don't want to help you by answering generic questions, but because I'm aware there is an active legal case going on and I don't want to stick my nose in and jeopardize your defense the case because I don't know the exact circumstances.
Any other ways that I should be aware of?
Unlikely.
In a typical corporate environment running Windows where you regularly change your password on the domain, it's unlikely any other options would be viable (e.g. remote control) unless the admin knew your password. But as passwords are stored in encrypted format on the server, the only way an admin would know your password is if you gave it to them or if they were doing a security audit and yours was found via a dictionary attack.