Put it this way - there have been times where there were multiple claimants to the Papacy, each being quite well supported by factions of Cardinals and so on. Naturally these can be confusing.
In fact, to remove all doubt at the end of the last such period in Church history, the Western Schism, all the three claimants to the Papacy resigned and a fourth one was unanimously chosen by supporters of all three previous claimants. Since that fourth was unanimously agreed upon by those with the authority to choose, we can be safe in saying he was a true Pope.
Given that maybe a handful of people in all of Christendom, none of them of any great import or influence within the Church or having any role in the election of Popes, have challenged the legitimacy of JP2’s election as Pope, it is quite safe to assume that he too is indeed the true Pope. If his claim was not in genuine doubt during all the decades he reigned, it is not going to be in the future either. Likewise with Benedict 16.