I learned the same thing. What changed it was not the Internet, per se, but the instantiation of proportional fonts.

http://en.wikipedia.org/wiki/Sentence_spacing
"With the introduction of proportional fonts in computers, double sentence spacing became obsolete.[13]"

... and later ...

"Most modern literature on typography says that double spacing is wrong,[18] but some non-typographical sources indicate that it could be used on a typewriter or with a monospaced font.[19]"