his or her

In his latest Fox News column, Radley Balko writes:

It seems to me that a good remedy for most of today's contentious issues is to let everyone live his or her life as they please, so long as they do no harm to anyone else.

I find this sentence interesting, because the word "everyone" is singular, not plural, so it should paired with "he" rather than "they." However, since Radley uses the p.c. construction of "his or her," rather than the succincter and harmless "he," I think "they" is appropriate.