It states that Stances replace Spells, but doesn't say they "do not gain any spells or spellcasting ability, do not have a caster level, and cannot use spell trigger and spell completion magic items", which is commonly stated in other Archetypes that replace Spells with a feature.
Is this an oversight/error, or does it not make a difference that the caveat mentioned above is nowhere to be seen, and therefore I can't use spell trigger or completion items?
First up, I don't have the book so i'm going solely off your post.
It's a 3rd party book, so having different language is probably usual. If it says it replaces spells then you don't get spells. Being able to use wands only works because you can use wands that are on your spell list. If you don't have a spell list then you can't use them.
If you look at the Paladin Archetye "Knight Disciple," it has the spell replacement, too, but has:
Spell Familiarity (Ex)
Starting at 1st level, a knight disciple can use spell completion and spell triggers items (such as scrolls and wands) as if she possessed the ability to cast paladin spells, using her initiator level as her effective caster level.
So, that backs up MrCharisma's assessment, since Ambush Hunter doesn't get that same ability.