Bob,
I would say that if indeed this was a "tie" then no true takedown existed and thus not awarded.
Unfortunately (depending on your point of view) the rule book does not make exceptions to its wording or interpretations of scoring manuevers based on the conditions or situations such as those that you mentioned. In other words you don't get the close calls simply because another situation exists. If the kid was stalling, backing up, and/or avoiding contact then he should have been penalized appropriately for that action. To give a competitor a score that was not achieved properly because of those other situations violates the very essence of the rules.
Now as far as the attempted takedown itself. The easiest way to think about this is ... would that exact same position and situation be called a takedown 30 seconds into the 1st period? If you can't say 100% yes to that, then what happened at the end of that match wasn't a takedown.
Just my personal opinion.