Was fallacious too strong a word?
First, there is absolutely no reason why "this method" does not guarantee the same result that the Electoral College does. IT USES THE ELECTORAL COLLEGE. The same electoral college that has been used in every other elections. In the same way that States can apportion their votes any way that State law allows, the NPV is simply a creature of State law, and follows the Constitutional mandate.
Second, you make an assumptions about recounts that don't bear scrutiny. First, why would every State need to recount? Only those States in which it was in the margin of error would require a recount, and that, itself is unlikely (see the previous post on Margin of Error). Second, so what? You act as if a recount would be some terrible, and burdensome thing. Every State has a system of recounting, and most are quite efficient. As you noted, "recounts do happen at state and local elections", some States can get recounts done on election night.
Finally, you continue, as my mom would say, "borrow trouble" to maintain a system that is already broken. Change is good, when it is done for a good reason. Methinks there is an ulterior motive to your objections? Just a thought.