Is iTunes required for iOS7 iPhone to trust PC with Windows 7?
Definitely yes. You must have iTunes installed in order for the &quot;Trust computer&quot; option to be remembered.
What you can do is the following:

Temporarily install iTunes, do not run the program itself on your computer

Connect the iPhone and tap &quot;Trust&quot;

Go to the newly-created Apple Lockdown folder on Win 7 it is found here:
C:\ProgramData\Apple\Lockdown

Copy the whole folder and paste it to a location you can remember (i.e. PC Desktop)

Fully uninstall iTunes from your computer

Install the iOS drivers without installing iTunes (these drivers are needed in order for your PC to correctly recognize the iPhone

Restart PC if needed

Navigate to:  C:\ProgramData\

Add a new folder named &quot;Apple&quot; and inside it paste the &quot;Lockdown&quot; folder along with its contents.

This will keep your iPhone trust setting without the need for iTunes being installed