Incorrect.
You need F-15 installed to install TSHv2. However, if you use the one-click installer (or the coming-soon TSH release) you do not ever need JF-15 installed. Once the Iraq Paq is installed, JF-15 does not need to be installed.
Nano,
It sounds like you are loading a mission for which you do not have the appropriate objects installed. Since I believe the one-click installer places the standard TSH objects into your JF-18 install, I'm not sure why you are getting this message.
What is the specific mission that's giving you errors? Do you get the errors with other missions?