Unlocked skills sell at skill sellers?

I unlocked Phoenix and Flame Burst with Balthazar Reward points with my PvP Elementalist, then I started Role playing Elementalist and when I got to Lion's Arch I found Phoenix and Flame Burst were available, but when I looked on GWW, it said that Phoenix and Flame Burst were not available in Lion's Arch. I know that if u purchase a skill, it becomes available, but does it work with Balthazar Rewards too?

Are skills unlocked with Balthazar Reward points available at skills sellers?

EDIT:

You can get any unlocked skill (barring Elites) from any trainer from the respective campaign. Therefore, if you unlocked Liquid Flame, which is a Nightfall skill, using Balthazar faction, you can get it from any NF trainer or by using a tome. However, you wouldn't be able to purchase it from the Prophecies or Factions trainers.

Thanks, I just found it on GWW too.

http://wiki.guildwars.com/wiki/Unlock

Second Box: Benefits of Skill Unlocks for PvE Characters