Are you saying that every time someone does a 301 to a new domain the trust is reset?
No, not EVERY time. However, Google has said that they "reserve the right" to reset a domain's values to zero when it changes ownership.
It's worth reading some of the past discussions here on the topic. People have definitely had the experience, and others not. Try a Site Search
[webmasterworld.com] to surface relevant discussions. Be wary of the differences between these scenarios that new owners of a domain have discussed here. These are the kinds of details that can make a difference:
1. URLs and content remain stable for many weeks
2. URLs remain the same, but some new content is added to the pages
2. URLs remain the same, but some all new content is created for those pages
3. Existing URLs remain the same, but new URLs and text content are created
4. Existing URLs remain the same, but new URLs and content with outbound links are added
5. Both content and URLs change, but the domain still remains the same
6. After a waiting period of several weeks, existing content and URLs are redirected to a different but established domain.
7. Domain name is immediately redirected to a different domain, and all legacy content is also moved
8. Domain name is immediately redirected to a different domain, and all legacy content is just gone
From what I can tell, the farther down that list you go (roughly) the closer you get to having everything reset to zero at Google. What they want to prevent is people using a newly purchased domain merely to boost the rankings of another domain.
Do they always succeed? No, not at all. But that is the goal, as I understand it. So you want to send this kind of clear signal: "Yes, I am the new owner but I am only going to pick up where the previous owner left off. All existing traffic is being well cared for."