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A trust model is just a map of who trusts who, when and in what circumstances. It claims at least authoritative integrity with respect to identity, meaning, you are actually trusting who you think you are trusting (see identity dispute, interwiki identity standard, and faction - the latter for collective and alleged identity).
It is not reputation although positive regard, informally called "reputation", can play a major role in deciding whose assertions to believe, or at least which to investigate first. However it does not establish authoritative integrity - that takes an audit process, and that process has a form of investigative integrity which is different.
Trademark, standard labels and anything that you can audit is believed to have some degree of this integrity, or people wouldn't act one way when they saw the mark/label, and another way when they don't. Brand management is the active attempt to interfere with such integrity measures.
To understand the contrast, consider what happens when you see a term on a label like "fun" or "new" or "more" or "clean" on a label. There is no control or trust model behind these words, so you dismiss them as propaganda. This makes it actually impossible over time to use these words to mean what they mean in the dictionary.
See repute and interwiki identity standard and faction for some related concerns. Probably any trust model is mostly factionally defined, as acts that cause one group to trust you more will make others trust you less.