My guess is that either they fired the current teacher or that teacher quit and they need to fill the opening immediately so the kids don't get behind in their studies. With a teacher gone and no lesson plans, what's a substitute to do ... esp. if it takes a few weeks to get a teacher in! I'll bet that's why they're so hot to get a replacement.
They may have looked at other resumes and felt yours was the best fit and decided not to interview any others until they checked out the "best candidate" for the job.
Red flags ... if they make you sign an extended contract that doesn't give you the option to leave w/o some sort of financial penalty, then maybe. Otherwise, it sounds like they need someone quick and your resume was the best fit for them.