Is it possible for popups to come up while a computer is in sleep mode?

I went over to my boyfriend's house to hang out after he got off work and went to use his computer. It was in sleep mode, so I hit the power button and it turned on. The current tab open in his Opera was a porn video that was in the middle of running and resumed when the computer turned on. The tab before it that was minimized was the homepage of the porn site. I could click the "back" button and go one page back to the official home page of the porn site, not the video home page. And the video that was playing appeared to be a tab that opened when one of the video thumbnails was selected.

My boyfriend swears that he did not look for this, that when he left his computer that morning, he had been on 4 Chan (a shady anonymous message board) reading about video games. Someone had posted something about an actress appearing in something, so he googled her and her porn site came up, so he closed the window promptly.

He swears up and down that he has no idea how it got on his screen. That he set his computer aside and went to work. It had been in sleep mode when I found it, because it wouldn't respond just when the track pad was touched or clicked. I checked the energy saver for sleep mode and the display turns off after fifteen minutes, but the computer is set to never go into sleep mode. There was no browser history in his Opera internet browser.

I really want to believe him and he's always been incredibly truthful and trustworthy, but I'm not sure how this could be possible unless he or someone else was on his computer and brought up the site and video and then put the computer to sleep while the video was running.