I understand exactly where you are coming from, Comrade, it is a very pertinent question, an inevitable question, I would say, for anyone seriously trying to make sense of the crisis.
I agree with Matthew that there is a certain element of mystery involved that can only be resolved with the full weight of the Church's Authority.
However, in the meantime, the following teaching of St Robert Bellarmine certainly provides a "coherent defence" of this position of a Pope with doubtful orders being Pope nonetheless:
Two things can be considered on Bishops: Firstly, that they hold the place of Christ so for that reason we owe obedience to them... Secondly, that they might have the power of Order and Jurisdiction. If it is considered in the first mode, we are certain with an infallible certitude that these, whom we see, are our true Bishops and Pastors. For this, neither faith, nor the character of order, nor even legitimate election is required, but only that they be held for such by the Church... Now if this is considered in the second manner, we do not have any but a moral certitude that these will truly be Bishops, although it is certain with infallible certitude that at least some are true, otherwise God will have deserted the Church... - St Robert Bellarmine, De Controversiis: On The Church, Bk III On The Church Militant, Ch X On Secret Infidels
Isn't that interesting?
Yes, that is interesting. I have to admit when I come across valuable quotes like this, I have to reread it a couple times and then follow with the source and then look for commentary. I have not come to any hard conclusions at this time. There are usually distinctions that have to made.
What does "character of order" mean? Does it mean these true bishops and priests can be lacking the sacramental character of Holy Orders? The mystery continues...