I tried doing a little research to help prove the history of this guitar, basically trying to "screen match" it.
The guitar that Petrucci is playing/holding in the pics on the eBay page is definitely the same guitar up for sale, so at the very least, Petrucci has played and signed this guitar.
Unfortunately, the quality of the Another Day music video makes it impossible for me to say one way or another whether it's the same guitar. It's seen briefly, and it's washed out in light. So that's a bust.
So I tried matching it to the old Another Day acoustic video of just JLB/JP, which is the same make of guitar, although I'm not sure if he only had one of them, or a few. The quality on that is quite poor too, although there are close up moments where I can see details, and to me it does not appear to be that same guitar. I'm not even sure if that's relevant to the discussion, and that's just my opinion, not to be considered proof.
I hope this doesn't come across as a witchhunt MtjG, as it's a nice guitar, and I would love to be able to confirm this as real, as this is possibly a great piece of DT history!
At the very least, it's a nice acoustic.