I’ve been skeptical about the “if the class is not offered at _____, it won’t be held against you” claim for quite some time now. It is similar to the idea that the personal statement can only benefit applicants; it does not work against them. Or, for example, the concept of required or recommended coursework. Having not completed the recommend coursework for a program theoretically won’t be held against an applicant by nature of being referred to as recommended or encouraged rather than required; however, that does not mean that those who have completed the recommended coursework will not gain a noteworthy advantage.
I would see that claim as more realistic in cases such as TAG or other guaranteed admissions where students are not competing because I have a hard time believe that universities are truly viewing students who have not finished prereqs as equally competitive as those who have completed them with high marks simply because one college did not offer specific courses. It might not be fair, but the admissions process is rarely perfectly fair. There are always applicants who simply had more opportunities available to them than others.
With that being said, @Mont2LA, I would say that the fact that you have completed a statistics course works in your favor. You would still have to take another to satisfy the requirement at UCLA; however, having taken that course shows that you are competent in the subject so I believe that you have an edge over those who haven’t completed any comparable math courses. The PoliSci department has to know how unreasonably picky they are being about that requirement.