The encumbrance limitation of the fly rules were removed from pathfinder.
There is not (and wasn't in 3.5) a limitation on Medium or Heavy armor in the fly rules.
The only limitation holdover from the 3.5 fly rules is Barding which is a subset of armor. It does not apply to the Armor or Load rules in any way. The section in the load rules that state it applies to Armor does not apply to Barding (at least, not without a FAQ stating it does) because Barding is a sub-rule not the general rule that the Load rules point to.
Frankly, they should do away with the line in Barding. I believe it is a remnant that escaped them in the move to PF. Limiting natural flight to light encumbrance wasn't a good rule in 3.5 as it was needlessly complicated.