Dr. Mustafa Zayd rejects this claim in his book النسخ في القرآن الكريم, volume 2, pages 177-180 (items 962-971) on the basis of no contradiction. He shows that Ash-Sha`bi and Al-Hasan, who are claimed to have backed up this claim, actually meant that this is a case of license after resolution رخصة بعد عزيمة. He asks this simple logical question: What happens in debts where the two parties do not trust each other? Clearly they have to register the debt in writing. Thus, 2:282 remains valid in this case and that means it was not abrogated!
By the same token, Dr. Zayd asks the question: what about the pawn clause in the verse? Does a pawn abrogate the need to write down the debt? Why was that not discussed? The fact is the pawn is contingent upon unavailability of a debt writer, as may be the case during a travel. So, is the relaxing of the requirement to write the debt contingent upon mutual trust.
It seems to me that the exception based on mutual trust applies only to the pawn, not to writing the debt. The only exception to writing the debt (other than on-going business) is travel or lack of a writer. If these conditions are not there, writing the debt is mandatory whether people trust each other or not. IMHO, this is one of the cases where God mandates something that prevents practical problems because it would be awkward or offensive for some people to require it if it wasn't religiously mandated.