I didn't claim that it could be true, as I did in fact state that I know of no logic that accepts "A or not A". The argument was solely about what the law of the excluded middle is. IOW, law of the excluded middle != law of noncontradiction. Classical logic accepts both of these laws, intuitionism only the second.

edit: looking at Wikipedia does seem to indicate that there might be systems of logic where "A and not A" might not be valid (paraconsistent logic), but I haven't really looked into that, and I don't know how much such systems are used.