Hi, it's strange! because I have a free version of airtable and I can do it. 

with the private mode, I can fill out the form without an airtable account. 

Have you share the form in the correct way? 

Thank you for your reply. Yes, I did the same but nothing. I even tried creating in another view but it will not work.

Have you used the new format of the form? if yes, you have to deactivate this feature

I'm stumped. This feature was also off: 

I'm sorry if I'm asking so many questions, when you published the form, have you select "Only users with base access"? If yes, this is the problem. You need an airtable account. You have to select "Anyone on the Web"

and to test it on your form with "Assignee", you need to remove this field on the form, because you can't show the airtable accounts of  your assignee

That is exactly what I changed and yes, it worked! Thank you!