Why does one type of tethering obstruct MTP while another doesn't?
It's probably because ClockworkMod Tether is using a different USB mode (getprop sys.usb.config) which has MTP mode enabled too.

native USB tethering: sys.usb.state = rndis,adb (where rndis is the internet tethering interface)

ClockworkMod Tether: sys.usb.state = rndis,adb,mtp

You could try to enforce this yourself when using native tethering by doing this: 

setprop sys.usb.config rndis,adb,mtp


But this could require root on your phone.