When I pick the sword skill my character doesn't start with armor granted through Master of Arms or the shield granted through Shield Bearer. Tested with Archeology and it still gives the Fedora. EDIT: I've tried more builds testing. I can't figure out what combination is bugging it out. I'm trying to run Swordplay, Crossbows, Shield Bearer, Artful Dodger, Master of Arms, Perception, Burglary.
You only get the armour and shield if the majority of your skills are 'warrior' type. The example you have given has more 'rogue' type skills (crossbow, dodger, perception, burglary) than 'warrior' type (sword, shield, arms).
I do have to say that's a bit odd, but it does make sense. It should have a way to tell you in game how the skill added items work.