Barkskin doesn't grant an AC, just
Say you AC would be 13 without barkskin. You cast barkskin, it's now 16. With yours your AC is 16. Okay.
You pick up a shield. With barkskin, you base AC is now 15, so is raised to 16. With yours, it becomes 18.
You gain a +2 cover bonus to AC from one target. With barkskin, your 15 becomes a 17 against that target, 16 against everyone else. With yours it becomes a 20 vs. them, 18 vs. everyone else.
Yes, it's not the most intuitive spell because while it does exactly what it says, it does something unique. It does a different thing then just granting an AC. My guess as to why is that it has no chance to become part of a power-combo that moves outside of bounded accuracy, but it doesn't really matter why, just what the spell does.