Aside from that being a really bizarre use case, it's an interesting phenomenon. My guess is it's not meant for simultaneous output, but that still doesn't really explain why it's doing it.
My Premiere XL4 gives the "HDMI Connection Not Permitted" message occasionally through HDMI, but it either quickly clears, or hitting Live TV and going back to TiVo Central will clear it. I just chalk it up to the complexity of my setup, which has the TiVo outputting to video processor, which then outputs video to my TV, and audio to my AVR, all via HDMI.
My Place: Premiere XL4 Lifetime 3/26/13 XFinity
3 TiVo Mini's on MoCA
Formerly Win MCE 3TB Ceton4 XFinity
Parents: XFinity Motorola AnyRoom DVR
80 HR Series 2 Lifetime 4/11/04 DEAD as of 11/2010