Calling it "pseudo-Monte Carlo" is like calling a landline phone a "wired cell phone". It kind of misses the point.
I really wish people would stop trying to find ways of calling their algorithms "Monte Carlo" just to make their work sound fancy. All it really achieves is it makes them avoid thinking about how to solve the problem. Monte Carlo isn't a universal hammer. First you're supposed to show randomness actually helps you gain something, then you're supposed to start using it.
I use that trick a lot, for instance with Euler problem 307 I could not find the answer easily in an analytical way, did the simulation, found an approximate answer (to within 6 decimal places or so), used that to figure out what I was doing wrong and then computed the real answer.
Some may see that as cheating, but it works wonders and not just on that particular problem.