Sure, but when "but" is used to qualify "can agree", it is surely being used as an adverb? ... and if you scroll down the link you posted, you'll see the "only" meaning I posted in relation to use of the word as an adverb.
In the phrases we are discussing, the word "but" surely is not being used as a conjunction (which is what your posted material relates to), is it?
I'm really not arguing, or wishing to argue, and can see that this is one of those situations in which people have differing views which they individually believe are 'correct'. All I'm doing is reporting the way in which I have used the word/phrase for the many decades of my life to date!
There are clearly variations in usage if, as I illustrated, some sources give essentially the same meaning for "can but agree" and "cannot but agree".
It's perhaps a bit like the trans-Atlantic difference between "could not care less" (UK) and "could care less" (S) - although in that case the latter seems so daft to me (in relation to the intended meaning) that I do my best to ignore it (but still shiver whenever I hear it ).
Kind Regards, John