Wouldn't the original sender be occluded by the group email address?
Eg: Help.me@ext.org => group@company.tld => tickets@company.org
Therefore the ticket is created for company-group@googlegroups.com or similar?
But you raise an interesting use-case. I've a solution in mind, needs to get my tools (my code is at work).
Essentially, we can use my rewriter plugin to change the sender to the original by changing the headers!
https://github.com/clonemeagain/plugin-fwd-rewriter I'll have a look in a few hours (it's 0643, I try not to code this early). But if you're sufficiently caffeinated and willing to try, it's a public repo, make a pull request.
The dark magic? Well, I call it that because the settings are dangerous.
https://support.google.com/a/answer/1346934?hl=en
Basically you can use the content compliance Configs to change things.. even headers.
However, if you've tried commenting out the check, and it didn't work, then it's not that! So don't go breaking your whole email system on a hunch by some forum weirdo (me).
Maybe check your outbound email logs, perhaps it is sending it, but the group is ignoring it because the ticket system isn't a posting rights member?