The only urban legend I heard about the origins of aspirin is that it was originally snorted, hence the name.

Allow me to clarify: in french, "aspire in" could mean "snort it in", though in a goofy brand-name-ified sort of way. This is something that my french high school chemistry teacher served the entire class in the most serious way possible.

"Aspirate" is also an English word which just means to breath something in. Sounds medical (so not generally used) but not in an awkward brand-namey way.