That's a weird one. I can tell you from a hardware perspective that the MPEG decoder chip (the one with the IBM logo on it) can overlay on screen text/graphics over a background video but usually what happens is that the background video is one of the animation "loopsets" which are designed not to clash with the on-screen text colours.

Given that you have seen this on two TiVo's suggests it is not a hardware fault but seems that a glitch in the software is causing the last played video not to be replaced with the appropriate loopset.

Why this is I can't say as it is not my area of expertise, but just offering an insight as to how the MPEG decoder chip works in this respect. FWIW I can also vouch that the startup animation fix has nothing to do with this as I have done the change to several TiVo's and not seen the quirk you describe.