You are just misunderstanding how hexproof works.
Hexproof means it can't be targeted by the permanent's owner's opponents, not it can't be targeted by whoever gave it hexproof's opponents.

I casted Loran's Escape targeting Scurry Oak

Scurry Oak gained "Hexproof (This permanent can't be the target of spells or abilities your opponents control.)"

My opponent then casted Rosie Cotton of South Lane

My opponent was then able to target his Scurry Oak with Rosie Cotton of South Lane's ability regardless that I gave the permanent Hexproof

My opponents then looped +1/+1 counters onto Scurry Oak and won the game from this play.

I believe this is a mistake and my opponent took an illegal game action.

Hexproof means a permanent can’t be targeted by spells or abilities that your Opponent controls.

If it gave Shroud it would work the way you were expecting

No bug, you just don't understand what it means to give a permanent hexproof. It is the permanent's controller's opponent that cannot target the permanent. Which means, giving hexproof to your opponent's creature makes YOU unable to target it with spells or abilities.

I casted Loran's Escape targeting Scurry Oak

Scurry Oak gained "Hexproof (This permanent can't be the target of spells or abilities your opponents control.)"

My opponent then casted Rosie Cotton of South Lane

My opponent was then able to target his Scurry Oak with Rosie Cotton of South Lane's ability regardless that I gave the permanent Hexproof

My opponents then looped +1/+1 counters onto Scurry Oak and won the game from this play.

I believe this is a mistake and my opponent took an illegal game action.