That's a funny standard, and not that I disagree--quite the contrary--but once you get an undergrad in engineering you're an engineer right? Sure, there is an expectation to pass the FE exam but is being employed as an engineer a requirement to "be an engineer"?
I hear a lot of people with a BS in Comp Science that call themselves computer scientists which seems mostly inaccurate too.
It's just odd, these titles and what qualifies you to call yourself a thing.
It's just about how it's colloquially used. Even in industry we mostly call ourselves software engineers / developers, but if people say "Computer Scientist", especially in the context, it's generally understood you didn't mean PhD level research.
Mathematician, OTOH, does kinda usually imply that, or at least implies you do something that likely requires beyond undergrad level education.
Sometimes people differentiate by, for example, saying "research mathematician" but I think the meaningful distinction is: do you spend (an appreciable fraction of) your time creating new mathematics...
