This is a question of semantics. As such, I'm afraid to say that I can't discriminate which of the two arguments is more foolish - they are both equally so.
Okay, it depends on if you're talking of speed or velocity. If you're thinking about speed, then it's positive always. You can't get a negative speed.
If you're thinking about Velocity, and your example implies 1-dimensional velocity (which means I don't have to write a few extra paragraphs, I think), then one direction is defined as positive. That means that movement in the non-positive direction would, indeed, be negative velocity.
My answer, is to stop arguing and recognise that you're arguing over a vaguity in wording. "Negative miles per hour" is valid, if and only if you are working with vectors and thus if and only if it's velocity you're on about. Otherwise, if working with the scalar speed, it is nonsense.
Does this answer your question?