No FREE recount. Loser pays per precinct recounted, on a sliding scale. < 1% has one fee, < 2% has a higher fee. You might be correct on no ability to petition for recount if margin is > 2%. I'd have to look at the statute again to be sure.
IIRC, the linked article said free at 0.05%; between 0.5% and 2%, it’s $5/ward.