The rule says nothing about the deep back CAN receive the snap. Shoot, using that criterion, ANY back CAN receive the snap. CAN means legal to do so. It says he must be IN A POSITION to receive it. If he is three yards off to the side while someone else is closer and directly behind the center, then the closer, direct person is the one in a position to receive the snap, not the deeper, wider back. You are interpreting the rule to say ANY person eligible to receive the snap is in a position to receive it.
The reason I keep bringing up the A-11 offense is because that is EXACTLY what the current writing of the rule was designed to prevent. And it was written to describe two, UNIQUE formations, a FG formation and a scrimmage kick formation. It was not meant to be a blend of the two. And yes, I am SURE of the intent because I sat with one of the Rules Committee members before he went to Indy, and we discussed this very thing. Now, the final wording became a generalized bastardization of what we discussed, and therein lies the problem. But read the rule, it says "either", and goes on to describe two DIFFERENT formations.
You are saying if ANY back lines up 10 yards back, then it is a scrimmage kick formation, regardless of the position of the other backs, as long as they are not under center. That was NOT the intent. The intent was to describe two unique formations. If a team is a FG formation, then the holder must have his knee on the ground, and there must be a kicker no more than 3 yards behind him in a position to attempt a place kick. If they are in a punt situation, the punter must be 10 yards behind the line. That is the rule in the vernacular. Unfortunately, they didn't write the rule in the vernacular, they wrote it to conform with other definitions, and in a generalized form, thinking that any official with some common sense would not confuse the two formations.
Let's take your definition to the next level. QB in a shotgun formation 5 yards back, tailback 6 yards behind him. By your definition, this is a scrimmage kick formation, because there is a back more than 10 yards from the line that COULD take the snap. After all, what prevents the QB from stepping aside after the count and letting the ball fly back to the tailback, or the snapper from just snapping over the QB's head?
If that were true, Coach Bryant would be back in business!