I use both an Insignia Blu-Ray player and a Sony DVD-Recorder in my system.
Does anyone know if it's possible to program a SONY RM-VL600 to operate both devices? I use the dvd function for the Sony unit, but how can you use the Insignia remote to "teach" its on/off function? Am I correct in assuming that a remotes power button cannot be taught? No point keeping the Sony remote if I still have to use the Insignia to watch Blu-Ray disks.

I don't know about the Insignia Blu-ray.

But the RM-VL610 can do this, and I assume the VL600 has the same capability. You can program as many DVD player/recorders to 7 devices (except the TV) as needed, just enter the listed code. And if there is no code available, teach a complete device to one of the component devices. I've done this for a media player which has no code available. And yes, including power button.