Let’s change the situation. Assume I have a large linear program. I have a solution vector x. I couldn’t be bothered checking that all the constraints hold, but I randomly sampled 100 of them and they seemed okay so I declare that my solution is probably feasible. Would you ever write that in a paper?
As I said above, this is a philosophical question. Not a technical one. You can come up with a variety of statistical arguments. My position is that they are misleading. If you do not have relatively complete recourse then you cannot claim to have found a feasible policy, and therefore you cannot claim to have solved the model.