I don't know if this is functioning as intended or not, but I received only one set of barding after allocating my companion's skill points in each type.

Time: ~10pm EDT
Frequency: once/twice
World name: Lamia
Character name: N'aemingh Wey
NPC name: n/a
Monster name: n/a
Class/Level: WAR 50
Party or solo: solo
In-game time: unknown
Area and coordinates: New Gridania

Steps:
1. Use Reagan Pepper to reset chocobo skill points
2. Allocate all points to Attacker — received dragoon barding
3. Use Reagan Pepper to reset again
4. Allocate all points to Defender — no barding received (PLD)
5. Use Reagan Pepper to reset once again
5. Allocate all points to Healer — no barding received (WHM)