What is shown there is a "difficulty 1 hash" being reported, which is analogous to a share being reported in a pool.
Exactly. Which means 'difficulty 1 hash 1' is analogous to 'shares 1 hash 1'... And this is precisely what we see on 'Summary' tab - Accepted 1 (1). There is no point in accepting 'Difficulty 1 (1), of course.
Just as a small fraction of shares are valid solutions to a block, a small fraction of these hashes are valid solutions to a block.
I don't get this at all.
There is only one valid solution to a block, not many. Whatever small they are, shares are always
part of a valid solution to a block. Otherwise, they wouldn't be shares at all, because they would be shares of zero!
This explanation is rather unconvincing, Kiv. Sorry.