When the installer connected my TV he said they were told to use component cables in lieu of HDMI because of distortion. He could have told me anything but is it true.
No. HDMI is all digital end to end. You either "get" the picture or you don't.
Component cables are analog. While they will deliver the same 1080i resolution to your TV, they are not digital end to end and thus are potentially subsceptable to distortion. On the upside, you get a picture always -- even if the signal quality is degarded.
Many installers recommend the component cables because they have less issues with them -- some TV's seem to have difficulty with the HDMI signal from the Motorola STB's and result it no picture being displayed. Best advice is to try it -- if the HDMI connection works for you, use it. If not, stick with component.
Some aspects of the HDMI interface are not as tightly specified as they probably should be, and the result is HDMI isn't necessary quite HDMI. This tends to happen when you try to design an interface that has to work across both a number of platforms, and number of vendors.
This forum has many posts about HDMI issues. One Verizon guy even referred HDMI as Highly Deceptive Media Interface. The reality is HDMI does work for most users, but with several million FiOS HD customers, if .1% don't work, that translates into a many thousands.
As the other poster has said, it is simply much easier for the tech to go with Analog component cables, then to try HDMI, and then try to trouble shoot the HDMI connection if it doesn't work as expected. From my perspective that is a poor excuse, but it is probably an accurate presentation of the issues.