This is a good question, but very complex as members of a partner forum explored recently.
As with many aspects of relationships affected by AS, the matter of trust may vary wildly from one couple to the next, but I’ll share the thoughts that I shared, that are related to my own experience.
My comment within the forum was that “I think their trust (AS partner) is closely linked to what their values are and how they believe we are complying with those.“
My recent experience was with a partner who had values linked to finances and asset building, he was a hard worker and honest in his business dealings, but even though I was as honourable and transparent as I could be and contributed as much as I could and pulled my weight, I didn't let him be “in charge” of my stuff, nor did I follow his directives and therefore he persistently demonstrated suspicion towards me.
It was crushing because I'm sure I contributed to our shared lifestyle far more than he gave me any credit for, and all the while my own asset (home) was left to slowly run-down because I didn't have the funds to maintain it.
So, as I said in my initial comment, it seems to depend on what they value and how well they perceive that we are complying with that as to whether they trust us.
I'm not saying everyone’s situation will be the same. I know my ex-husband (I was married to him for 20 years) never seemed to trust me, but it wasn’t about finances or assets with him. He was very ego-centric, and having me in his space made him feel very threatened, which I think many other partners find is true too. We expose their poor attitudes and behaviours and hold them accountable which they don't seem to forgive us for. I never felt like I had any credibility in his estimation, which tied in to his trust in me.
Added to this is something I wrote about not that long ago, about how they seem to build up a perception of us based only on our reactions or negative responses to their poor attitudes and behaviour and they don’t balance up their perception of us by all our good qualities and all the amazing things we do do, particularly for their benefit.
These seem unnoticed, and seem to be irrelevant to them and their estimation of our trustworthiness, or not.