@as1799, there may be reasons for choosing ME over CS, but this is definitely not one of them.
I disagree with this as well. If you end up loving programming, and despising Physics, an Engineering degree will ground you in something you hate - that’s not better, that’s worse.
I think @NeoDymium is trying to say that if you’d like to program in an Engineering environment, on Engineering systems, that you’d be better off choosing ME as your major and picking up whatever programming skills you might need. That I would agree with. And I would also agree that you’ll cover a lot more ground in an Engineering degree.
If it were a choice between Computer Engineering and CS, I think I’d agree with the comment about grounding you more. Computer Engineering will give you a lot more background in how computers work than a CS degree. But ME and CS are two pretty different things. In Engineering systems, both will be involved, so knowing both would of course be an advantage, but you might end up really liking Web programming and building web sites. In that case, you’ll have learned a whole lot of difficult Engineering material that you won’t need at all. It will be character building, but you could put that extra effort into advanced CS courses.
One other thing. If you finish a Mechanical Engineering degree and then decide that you want to go into straight business programming, that will be an easier transition to make than if you do CS and then decide you want to go into Mechanical Engineering after graduating. Maybe that’s what @NeoDymium was getting at.
If you’re really on the fence, I would start in ME, and take some programming courses as early as possible. But I would take into consideration how difficult is to move between the two majors at the schools involved. It might make more sense to start in CS, but also take the intro ME courses in sophomore year, if that’s possible.