This what's called the "emphatic form." You might use it if someone has said the opposite: A: He doesn't have funny hair. B: No, he does have funny hair. Or you might use it to show contrast: He's a handsome man, but he does have funny hair.

From my understanding, as a native speaker of English, it's correct to say: "He (third person) has funny hair." If, however, you are emphasizing, in an affirming way, a response to the statement, it could be: "He does have funny hair." When you add the verb 'do' in the statement, 'has' becomes "have" in the third person (he). Anyone else . . . ?

To make it sound like an even greater affirmation he might say: He does indeed have funny hair. He certainly does have funny hair. He most certainly does have funny hair. There used to be a cartoon with two little animals (squirrels I think) called Chip 'n Dale (a play on Chippendale) that would speak in an excessively polite and pretend-aristocratic manner. They might say something like "Indubitably, he most certainly does have funny hair".

We use 'does' or 'did' to give emphasis; it can be used similarly, in some cases, like the Russian particle же. Here, the emphasis is affirming or agreeing with the other person: A: I see him all the time at the store it's like he goes there everyday. B: I see him there all the time too, it DOES seem like goes there everyday. --- А: I thought you were going to the bank today? B: I DID go to the bank today. --- A: I think he has a problem with authority. B: He DOES have a problem with authority.

^^^ This *is* ^^^ :)