People don't have to consciously want to change the language for it to change. It's not like the differences between modern English and Victorian-era English are all because someone willed it. Usage dictates meaning, and I'd say the general public uses 'begs the question' as 'raises the question', whereas only people interested in philosophy use it as 'presume the answer' - essentially the latter version has become a sort of jargon regarding fallacies.

It's like the word 'irregardless'. As much as 'it isn't a word', it clearly is, because you know what is meant when it's said, and plenty of people say it.