It isn't. The "recharge happens at the end of your turn" is an -awful- counter-argument, enough so that it's really a proposed house rule. The Demigod 30th level powers starts with "when you have expended your last encounter power..." -- so that's when it happens; right then. It does specify when it happens, so making a ruling based on saying it doesn't is flat-out wrong. (houserule, sure. But good interpretation doesn't contradict the text).
"You must take the second reroll" is, in fact, an significant order of rules lawyering worse than the infinite combo. But it's not an awful literalist ruling.
The "The GM can limit the number of free actions on a turn" rule is clear, but fails on RAI grounds -- that rule is clearly intended to let the GM enforce reality so that you can't pile up free actions that would clearly take more time than your turn; they're free by ones and two, not twenty and thirty (the classic example is talking. Saying a few words, or even doing a quick strategy bit, is free. So is calling for someone's surrender (not with an intimidate roll, just stating willingness to accept it) or engaging in witty banter. OTOH, giving a philisophical speech that takes over half an hour of real time, or going on, and on, and on about strategy in the middle of a fricking battle? Not so much. In this case, however, the free action of rerolling your ranged attack roll is clearly not an action that takes significant time; it occurs in the split second between firing your bow and it hitting, so using this rule is an abuse (if an abuse used to coutneract another abuse).
Probably the best specific argument (but not necessarily the best general one) is that a reroll isn't an attack roll. So you can't reroll it.
The best houserule to deal with this sort of thing is to say that you can only ever reroll a roll once, unless you have a power that -specifically- lets you reroll a reroll.