If we're arguing semantics and whether or not Ichigo has said he will protect Rukia, then yes, Kakashi is correct but it's just such a worthless point to argue and run circles around. It's not as bad as the stupid heroine/female lead nonsense though, I just scroll past posts when I see that.
Even though I have a tendency to hold more strongly on to words than to speculate, as is part of my cautious nature, I still think there's far too much emphasis in these debates on what's being said and not enough on what's been done or implied, it's a frequent point of frustration for me.
Thank you for making the "protect" / "save" thing clear. It was one of those debate points where semantics were obscuring the reality, (although Kakashi is technically correct).
Ichigo has been protecting both Rukia and Orihime, for quite some time now. Not that I'm comparing the two relationships; you've discussed the differences very well already.