Verizon doesn't seem to recognize that PIP exists. If you have two tuners in your TV, you can run a line from a splitter directly into the second tuner. You will only get a very limited number of channels and of course no HD. A better solution is to talk Verizon into giving you one of the little free settop boxes they are providing people who don't want to pay for one. You can put it on the second splitter output and then into your TV. You will get many more channels and quality is better.
If you don't have two tuners, you can still use your old VCR as one tuner with a splitter.
Hope this helps.
You will only get a very limited number of channels and of course no HD (emphasis added)
Not True. If you have a QAM tuner you can get your local digital channels (which may or may not be HD depending on what they are transmitting) that are carried in clear QAM. You can also tune all the music channels, PEG channels (public, education, and government), and SD digital versions of your local OTA stations.