http://paizo.com/paizo/faq/v5748nruor1fm#v5748eaic9qto
As per this, things that replace Weapon Training with a specific choice of Weapon Training counts as Weapon Training for things that improve it. Would this mean I could take the Advanced Weapon Training Feat? I'd assume not as the wording of the question and FAQ generally sits around things that improve Weapon Training. But, the first line of the Answer says, "If the archetype ability says it works like the standard ability, it counts as that ability. If the archetype's ability requires you to make a specific choice for the standard ability, it counts as that ability." (Emphasis mine) However, that could be in direct reference to the question. But at the same time, would you consider Advanced Weapon Training to be something that improves Weapon Training as the effects improve your efficacy of the weapons of the group chosen? That's kind of a stretch, I'll admit, but still worth throwing out.
So basically:
1) Does an alternate Weapon Training count as Weapon Training for things that require Weapon Training?
- or -
2) Does Advanced Weapon Training Feat count as an improvement of Weapon Training?
If an ability is called weapon training (e.g. Arsenal Chaplain Warpriest, Myrmidarch magus, Sohei monk, etc.) it counts as weapon training and so is improved by something like gloves of dueling. To gain advanced weapon training options for these non-fighters they must either gain additional weapon groups to give up or to have some way to count as a fighter to take feats (like the Warpriest does.)
Alternate weapon training is trickier, if your alternate weapon training says something like "At 5th level, a dragoon must select weapon training with the spear group" then this counts as weapon training, the archetype simply restricts your choice of weapon group. If on the other hand, you have an ability that functions as weapon training (e.g. the crossbowman's "crossbow expert") or functions as weapon training with a little extra (e.g. the swashbuckler's "Swashbuckler Weapon Training") it does not count as weapon training for purposes of AWT.
This is, however, absurd and in a home game you can probably get the GM to just rewrite "crossbow expert" as "at 5th level, a crossbowman must select weapon training with the crossbow group".
So a dragoon fighter can take advanced weapon training with a feat, an arsenal chaplain warpriest can take advanced weapon training with a bonus feat, but a crossbowman fighter cannot take advanced weapon training with a feat nor could a swashbuckler regardless of archetype.
When the Weapon Master's Handbook and Armor Master's Handbook came out, I wish they did Errata for the Fighter archetypes that have Quasi-Weapon-Training to make them work with the new material.
This case was more towards the second. Archetype in consideration is the Learned Duelist, which forces Light Weapon Group for Weapon Training. That's what I was leaning towards after reading the FAQ and what my friend initially understood.
I've also pointed my GM towards this thread in case he wants to weigh in on the matter.
So with the case of Forced Choice/Alternate Weapon Training (Dragoon or Learned Duelist) you count as having Weapon Training?