What about trust?

That is not quite exact. Quoting Documentation/process/submitting-patches.rst,

> The sign-off is a simple line at the end of the explanation for the
> patch, which certifies that you wrote it or otherwise have the right to
> pass it on as an open-source patch. The rules are pretty simple: if you
> can certify the below:
>
> Developer's Certificate of Origin 1.1
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>
> By making a contribution to this project, I certify that:
>
> (a) The contribution was created in whole or in part by me and I
> have the right to submit it under the open source license
> indicated in the file; or
>
> (b) The contribution is based upon previous work that, to the best
> of my knowledge, is covered under an appropriate open source
> license and I have the right under that license to submit that
> work with modifications, whether created in whole or in part
> by me, under the same open source license (unless I am
> permitted to submit under a different license), as indicated
> in the file; or
>
> (c) The contribution was provided directly to me by some other
> person who certified (a), (b) or (c) and I have not modified
> it.
>
> (d) I understand and agree that this project and the contribution
> are public and that a record of the contribution (including all
> personal information I submit with it, including my sign-off) is
> maintained indefinitely and may be redistributed consistent with
> this project or the open source license(s) involved.

Whether or not a patch generated by an LLM qualifies for (a) or (b) is being debated, but authorship is not required to add a Signed-off-by line.