Собственно, сама нашла: James's parents were elderly, were getting on a little when he was born, which explains the only child, very pampered, had-him-late-in-life-so-he's-an-extra-treasure, as often happens, I think. They were old in wizarding terms, and they died. They succumbed to a wizarding illness. Ничего ни про "умерли, когда Джеймс уже закончил Хогвартс", ни про 1978 год.