Jeff,
I don't know the exact method used by Basis in your company to conduct a 'refresh'. However, I have never seen a refresh done whereby the refresh process MUST set the jobs to 'scheduled' status. This is typically a discreet step performed by Basis, either done manually or done via script.
The two programs you speak of are not really designed for refreshes, although I do know Basis people who like to use them for refreshes because they are quick.
In closing, YES, it is possible for Basis to exclude selected jobs from being set to 'scheduled'. You should approach the Basis manager and tell him/her that this is a business requirement.
Best Regards,
DB49