Quote from opt789:
You are making it too complicated. If you are short a Put, then you are short a Put, it does not matter what else you have, or when/why/how you did the trade. If the Put is an exercise candidate, per the formula I outlined, then you may be assigned. That is pretty much all there is to it.
Cost of carry is how much you pay to hold an option contract. The question is whether you can open a contract with one price to pay to carry it and then it turns out down the road that the price of carry goes higher. It's not true for the outright long calls or puts. The cost of carry there is predetermined and it does not change through the entire life of the contract. Can it change and actually go up for the long call/short put combos? Maybe the early assignment is not a problem at all because it does not increase the cost of carry for the combos.
And yes this is the question of whether the option theory is consistent for any type of contracts ( simple or complex ). Remember all option contracts are contracts after all and the cost of carry should definitely be included in them as part of the deal.