That is definitely not true if you get tivo that is the whole point is to get rid of set top boxes. At worst if they make you get a box then there is a digital adapter which is less than $10. But if you need 2 cable cards for the 2 tivos it is probably about $10 for the both plus the tivo subscription. Will you save that much?
As far the 4k the VMS and IP clients are only 1080 as well. Broadcast are also mostly is 1080 so you should be ok there. 4k right now is mainly with streaming services.