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Hi Josh,
Thanks for posting back and providing the detailed information.
There was a misunderstanding in my first reply. I thought you were using a Microsoft form (group form) to collect responses, but the fact is that you were sending a list form to collect responses and add data to a list. They are different features. This was my mistake.
Generally, internal users should be able to access the list form and submit responses without permission. This is expected behavior. Also, based on my test, no list or site settings can cause the permission error. In this case, I suggest you create a new list form, send its link to them, and check the result.
If the permission error still occurs, it may be caused by their accounts. I recommend you report the problem to your tenant admin or IT team and ask them to raise a support ticket via the Microsoft 365 Admin Center> Support> New service request. The support team there has the correct channel and resources to help you investigate more and find what exactly the reason has caused this problem at the backend.
Appreciate your understanding and patience.
Sincerely,
George | Microsoft Community Moderator