Common usage has it the other way around - 'begs the question' does mean 'raises the question', simply because that's how it's used. That philosophical jargon has it differently doesn't change that.
I'm usually sympathetic to that argument, but the origin of 'begs the question' is philosophical jargon, and the misuse of it perpetually reproduces itself from people hearing it being used properly, not understanding what is being said, and trying to parse the phrase to figure out what it means.
Since the phrasing is anachronistic, there's really no chance that they'll come up with 'asks you to accept as true' for 'begs,' and 'the conclusion' for 'the question.' But honestly, if you mean to say 'brings up the question' you should just say it, instead of reaching for an anachronistic pithy phrase or buzzword.
