I have a Linksys PAP2 VOIP adapter connected to a Panasonic KXT-30810, along with a Verizon landline. The setup works fine, has been for 3 years.
I expect your setup would work fine if you were using a Linksys PAP2. The problem is that your Magic Jack isn't isolated from ground, and is causing a ground loop.
Using the phone extender breaks the ground loop, solving the problem.
Another option would have been to plug the computer into an isolation transformer. These occasionally turn up on Ebay pretty cheap, intended to provide ground isolation to computers used for medical purposes.
