It would not have been physically impossible to fake the moon landings. Physics tells us that the moon landings could have happened, but it doesn't tell us that they couldn't have been faked.
But by picking over the details of a particular example you're missing the point. Surely you don't want to say that you can reject crazy historical claims solely because the proponents of those claims make outragerous claims in other areas too. If you think the moon landings are an exception, for some reason, then let's look at other examples. E.g. Holocaust denial.
