Officials here are not responsible for eligibility issues.

A couple of times I have had a coach complain that an opposing plsyer has exceeded the playing limit - I simply tell them that it's not in our area of responsibility and they need to have their AD file a complaint with the state associaion.

To answer the OP's question, there is not an NFHS rule that would justify allowing the late reporting sub at the expense of a T. The only option is using a time out as Rich suggested. If they don't have any time outs left, they can buy one at the expense of a T.

That said, as Rich and Adam said I would probably allow the sub if they reported before the end of the intermission between quarters.

Honestly, if I'm never told why they need to make the sub, I can't adjust.

If I'm told they need a sub because A15 is no longer eligible, I'm going to allow the sub. I think the spirit of the rules allow for this, just as they'd allow us to sub out a player who managed to DQ himself, injured himself or got blood on his jersey in the middle of the timeout.

OTOH, if they sub him out at this point, it may already be too late.

Nosebleed ...
 

Just tell the coach to punch the player in the nose.

Here's what we are to do in my state. We are supposed to remove the player as soon as we are made aware that they are playing in their 7th quarter. There is no in game penalty, but we are supposed to fill out a form. I am allowing a sub, even if they are late to the table.

So it is the officials' responsibility to keep track of that? That seems odd, but each state is different I suppose. The team that had to forfeit won the game that night by 30 or so, tough break

Actually, they lost by 2. ;)

I doubt that, but perhaps they just take the coach's word for it. I'd only take the word of the coach of that player. Opposing coach doesn't get to dictate this, IMO (unless the state says otherwise).