I believe trust and transparency are very different concepts - but both influence our behaviour towards others (people and brands).
The Evolution of Trust by Nicky Case uses game theory to illustrate how trust works in transactions. It's fabulous; simple, clear and fun - well worth a few minutes. Spoiler alert: there are three big lessons; (i) how you behave matters (to you and them), (ii) we need to protect against zero-sum games and (iii) depth of relationship changes everything.
Don't cheat - for brands and retailers that means stop communicating perfection where it isn't present
Nobody wins when the customer loses
Long-term relationships with many repeat transactions between brand and customer might be the best defence against 'cheat' behaviour from either party
Overblown sustainability claims and a constant stream of variable discounts are not helping on point 1 or 2. And a race to provide everything to everyone, everywhere, all of the time, combined with specific incentives for new customers which are not avilable to existing ones isn't helping with 3. Some sectors (e.g. insurance / energy) seem to have perfected this model now - such that is is always rational to switch supplier.
If we want to increase trust, we need to be playing the same game, with the same people - a lot. Not a different game with different people every time.