I don't think he admits anything. That wouldn't be very smart of him after decades of speculation on who wrote that song. What he says in the video is very suggestive though, to say the least. We can't know for sure who actually wrote it, but to me it's pretty obvious Jon was involved one way or the other. I personally don't think he merely sit there giving tips on chords or lyrics, or tweaking it a little.

Don't get me wrong, I love Skid Row and that's one fine album. But 18 & Life has a certain je ne sais quois the other songs on the album don't. Not that it means he wrote it, but it makes perfect sense if he did. That said, I'm pretty sure Skid's version is much better than a Jovi version would ever be.