She's a rising star in an extremely narrow niche. Consider the following. I am an American. The US has many exceptionally gifted chess players who would have some form of celebrity and name recognition within the chess community. One or more of which are likely from my state and city, as it's a fairly large one. And I know who absolutely none of them are. And I have the benefit of 24/7 access to nearly all of human knowledge in my pocket. And I don't know because I don't much care about chess, like the vast majority of people. Similarly, modern day students/adults/etc. can be up to all sorts of things in their lives and yet their school/employer/etc. will have no idea. Because why would they? Why would they have that particular information? Why would a portion of their own, independent, potentially busy lives be spent acquiring the information?
Now rewind back to before the internet existed. Beth's celebrity star rises entirely within the confines of the chess community and its publications. All of which are physical, typed productions that have to be physically produced and distributed. Such information spreads slowly. It's not until local chess aficionados start taking note and she starts picking up a bit of mainstream appeal that the school is really going to have a chance to pick up on things. It's simply not something you'd expect a basic suburban high school to know about by anything short of sheer volume or pure coincidence. And once that happens, we don't see this sort of excuse being bandied about any more. Beth is, presumably, absent with the knowledge and blessing of her school at that point.