"I have a boyfriend"?

I've never really given a lot of thought to women saying, "I have a boyfriend" to deal with overly-persistent men (unwantedly? unwontedly?).  But some women obviously have, and their conclusion is interesting (even if I'm not sure I agree with it):

Male privilege is “I have a boyfriend” being the only thing that can actually stop someone from hitting on you because they respect another male-bodied person more than they respect your rejection/lack of interest.

And I'm not convinced that that's why saying that would stop an interested man.  I think two other factors play into this.  One is that some women (most, actually, I think) value persistence, and see it as romantic that someone would keep trying.  So I think that keeps some men trying longer than they otherwise would.

The other factor I see is the subtext that I automatically read into bringing it up.  That is, that "I have a boyfriend" seems like a partial statement to me, and implies a second half, "And I'm happy being with him".

I can certainly think of cases where men implicitly devalue a woman's opinion on relationship matters, but I'm not convinced that this is one of them.