A few other parts of the game would support Vincent having Jenova Cells.
-Lucrecia's Cave-
Lucrecia appears, and in her tyrade she explains that the reason she never died is because of the Jenova cells that were put into her body when Hojo was exparamenting on Sephiroth. ((I still think it was Rape. I doubt there's any way Lucrecia could have honestly loved Hojo, but that's just me.)) This would explain Vincent's failure to die.
Also, the fact that he just up left with you at the drop of Sephiroth's name. You know why? Not out of any moral obligation like he would lead you to believe, no. For the same reason that Cloud chases Sephiroth around the world, the relentless power of Reunion. Reunion, the force that draws all of Jenova's little bits and pieces into one conglomoration, influencing the wills of all those who contain it. Even those of strong will are weak and frail before the will of Jenova. Look at how quickly Sephiroth fell to the corruption. Less than two days time, he went from a proud and confident soldier, to a craven madman bent on serving his 'mother'. (I call him a madman because he is a madman. He woke up one morning and decided to burn a village to the ground. I consider that madness. At least a little bit.)