The third picture is just a sample to show how bad the picture is when recorded at lowest TiVo quality.
That third picture has a very specific problem to it that isn't related to data compression. It has an interlacing issue. It appears to only be showing one of the two interlaced fields in the frame. It has its lines doubled-up, similar to the problem pictured in
the section titled "Single-Field Interpolation" here.It's possible that it's simply an artifact of the thing being in "pause" mode. Sometimes a "paused" picture does that. If so, that's normal. But if your regular day-to-day viewing of a TV show always looks exactly like that picture, then you really need to get it fixed. If that's the case, say so, and we can discuss possible causes and solutions for it.
Other than that, yeah, it looks like a typical overcompressed digital broadcast to me: Fuzzy. Muted color palette. Color channel is smeared.