I have to take a different angle from several so far. I think, grammatically, there's no reason to suppose that "he" meant "the driver of the car" and every reason to suppose it meant the pedestrian. It's only a force of habit that would cause someone to jump to the conclusion that it refers to a driver.
The most important reason that "he" doesn't refer to the driver: The driver of the car was never mentioned. You said "a dude was hit by a car." Now, this doesn't totally settle anything, since it could be reasonable to use a pronoun to refer to an implied driver if context made that clear; if the last line had been "He was going 80 miles per hour," it would clearly refer to a driver (though it might be confused, at that point, with the driver of the ambulance).
The second most important reason (or is it really the first?) is that you had just used "he" in the previous sentence, clearly referring to the pedestrian: "I hope he recovers." If you had meant the pronoun "he" in the next sentence to refer to someone else... well, then you couldn't have used a pronoun, and would have to specify "the driver."
Now, the confusion is understandable since drunk driving is a frequent topic, so your friend's frame of reference leaped to a familiar conclusion. (But "drunk walking" most certainly is a thing; type "drunk pedestrian" into Google, and it autocompletes "hit by car," and the results are full of lawyers eager to advise you on what share of the blame might fall to the pedestrian in such a case.) Certainly, it could be helpful to have specified "the pedestrian" rather than use "he," but you were not negligent in using the pronoun.
(To other charges that have been mentioned: No, I couldn't call your account "incoherent." I understood everything perfectly. Standard capitalization and punctuation rules can be understood to be suspended in a chat-room context. And while "disclaimer" is more often used in a situation where you're qualifying something about yourself rather than someone else, it was perfectly understandable.)