TiVo HD-XL, splitter, signal strength

Here's a strange one:  My brand new TiVo HD XL works better with a 4-
way splitter on the coaxial input than with no splitter in the signal
path.

Scenario 1:
Comcast Coax Cable In --> 4-way splitter (radio shack) -->TiVo HD XL --
> Sony Bravia HDTV.
With this setup up I get a good clear picture with signal strengths of
60 to 80% (as measured with the built in signal strength meter utility
in - settings, channels, signal strength.

I was curious about how much better the signal strength would be if I
removed the splitter, so I removed it:

Scenario 2:
Comcast Coax Cable In -->TiVo HD XL --> Sony Bravia HDTV.
With this setup up I get No picture at all.  Nada. Signal strength =
0%. Black blank screen.

What the heck is going on.  I've tried this with different coax cables
over several days. Always the same result.  Looking through the forum
posts, I did come across a quick reference to "too much signal
strength" but this was not explained.  Has anyone seen anything like
this before?

Thanks,
Larry