OK...here is what I have found out....and I am updating this so that users in the future might be able to use it to help resolve their issues.
The permissions on the folder/directory where the database is located needs to have Modify access for all users who are accessing the data via the form.
My issue with some users getting the data and some not getting the data, but getting an error message was because some users inherited Modify access from the folder above the one I had created while others were added to a LAN group which had 'Read' access only. I was confused because all of the users were added to the LAN Group with Read access, but the users who inherited the Modify access over rode the Read access. Once I changed the LAN group to have Modify access, all users were able to retrieve the data by running the query and no longer received the error message. The query / connection must be using an administrator or defaults to a Modify user and therefore was having an issue retrieving the data.
I also tested this by having a user who could retrieve the data modify a text file I had stored on the directory (which she could do with no problem) and then I had another user who was getting the error message try to modify the same text file and got an error message that the file was read only.
So, giving users Modify access to the database location solved the problem.