Hi Michael,
> I would like anybody to be able to submit the form so that the survey is answered, but I don't want everyone to see the answers.
Yes, the workflow you want is fully supported. I recommend that you configure your sharing settings not through the Item Details pages in ArcGIS Online, but through the Survey123 website.
Sign into the Survey123 website with your ArcGIS Online organization account, and you will see all of your surveys listed. Select the survey you want to work with, then navigate to the Collaborate tab.
On this page, when you select the Submit tab on the left - this determines who can access, view, and submit responses to your survey.
When you click the Analyze tab on the left, this determines who can view the survey results on both the Analyze and Data pages (both in the upper right corner).
Hope this helps,