Actors:
TV Set: Advent HT3251A
DVD Player: JVC XV-N412S
Remote: Harmony 768

After I bought the DVD and TV sets I noticed that pushing the Menu Direction/Enter buttons in the DVD remote mode would also control the TV and either switch its Input or switch it Off completely.

Now the strange bit: This is not consistent behaviour. I haven't been able to figure out a logic behind it, but sometimes it works fine to go Menu Down on the DVD player and the TV won't react. Then I click on more Menu Down and -fssssst- TV is off. Huh???

I tried the factory remotes and, of course, the same happens (and also inconsistently).

Now, I was hoping that with the Harmony being a little more 'intelligent' there would be some work-around way to trick the devices in believing that they both have an exclusive relationship with the remote and not noticing that the remote is actually also having fun with the other (at the same time, too!!!).

Help, anyone?

Try playing with the "number of repeats" (under device > troubleshooting).

To expand on the logic behind jlet's suggestion (which is probably your best bet), basically the theory is that one of the two devices probably has an IR receiver that is slightly more or slightly less sensitive than that of the other device. By reducing the number of repeats on one device, the idea is that the remote will send a very short burst of IR signal that only one of the devices will be "quick" enough to catch.

Thanks jlet and spin-dizzy for your suggestions. I will give it a shot later today.