Yeah, that's why I specified, "major hurricane". I'm mainly concerned with hurricanes strong enough and close enough to do major wind damage in Houston (since the flood risk is pretty much year-round). So that can be narrowed down to landfalls between Matagorda Bay and somewhere east of High Island. Went back to 1900 on Wikipedia (I know, I know) looking for hurricanes in that window.
I missed the only major to hit in that area after Sept 13 (Ike was Sept 13), a 1941 cat 3(?) that came in near Bay City on Sept. 23.
Non-major hurricanes after Sept 13 were:
Oct 4, 1949 - (strong) Cat 2 at Freeport
Oct 16, 1989 - Cat 1 Jerry at Galveston
So the old wives tale is almost true after Sept. 23, but the 1949 exception is close enough to a major to require an asterisk. Darn, I could see our current odd season producing another exception.