There's always that little catch.
It’s no “catch” at all. The back-of-the-envelope analysis ignores “factors of order unity” due to integrals of variable quantities and geometry. It says that, whatever the details, it’s got to come out close to this. A factor of 2 is pretty close, and in fact amazingly close to my way of thinking.
The key point is that gravity will overcome any resistant force whatsoever, and this is evident from the basics of Einstein’s theory. Picking over Schwarzschild’s solution is not going to change anything.