This extract from a listing of idioms also comes from the Internet. I have copied those using the word 'beg', as they may all be of interest. The idiom is followed by a definition and then by an illustration. The last of them is the one under discussion and shows that, as Bean suggested, the common misuse may indeed become accepted!

'beg off' - ask to be excused from duty, get out of a task. Some people volunteer to work and then they beg off.

'beg to differ' - have a different opinion, disagree with. When I stated the cause of the loss, he said, "I beg to differ."

'beg your pardon' - excuse me, please do not be offended. I beg your pardon, but I am using this phone booth.

'beg your pardon' - what did you say? will you repeat what you said? I beg your pardon? Did you say you are Paul Newman?

'beggars can't be choosers' - people who receive free things should not expect the best. When they complained about the shabby coats, he said, "Beggars can't be choosers." (I think this is more a proverb rather than an idiom - dxb)

'begs the question' - suggests this question, leaves this question unanswered. "That's a fine idea," said the Head Mouse, "but it begs the question: Which one of us will put the bell on the cat?"