Can you screw roof metal directly to OSB between rafters?
No, you do not need to screw into solid lumber (joists, stripping,etc.). 

You’ll want to follow the manufacturer’s installation instructions, but here is a major metal roofing manufacturer’ installation chart for screws into plywood, OSB board, and 2 x lumber for wind uplift, which is on page 14:

http://pdf.lowes.com/installationguides/716702706866_install.pdf

As you can see, the thinnest material they recommend is 1/2” (7/16”) OSB board at 9” on center up to 24” on center. 

Be sure to follow their instructions in order to obtain the warranty.