For clarification, I just realized that the ODBC driver is based on the SQL version, not the GP version. This client is running SQL Server 2008 R2, so the correct driver for them actually would be the SQL Server Native Client 10.0.
What I can do is download the latest driver, because perhaps there is an update that will help to resolve this. Also FYI, the one particular computer where I had this issue was brand-new, so I don't believe there were any pre-existing drivers prior to my GP install.