It turns out the error has nothing to with direct table editing vs forms,
refreshing the recordset, or otherwise.  It had to do with a BIT column that
was accepting NULL values.

If we added a record in Access that did not explicitly give a value for one
of the two BIT columns, it would be assigned NULL.

Once a row had a NULL value for a BIT column, Access would refuse to edit it
(either directly or through a form), giving an error window that read:

"This record has been changed by another user since you started editing it.
If you save the record, you will overwrite the changes the other user made.

Copying the changes to the clipboard will let you look at the values the
other user entered, and then paste your changes back in if you decide to make
the changes."

This sounds like an Access 2007 bug.  At any rate, the solution was to give
a default value for the BIT column.  We updated any existing NULL values in
the BIT columns (which enabled Access to edit those rows), and changed the
definition to NOT NULL, to prevent the error from coming up again.

Hope this is helpful to anyone else experiencing this error.

 -Josh