The first quote seems to do a good job explaining.
However, the second one is about assigned duties by the employing company and I don't feel that is relevent.
The general rule regarding rest requirements is that if the other commercial flying is assigned by the certificate holder, it may not be conducted during a required rest period.
Key here is "assigned by the certificate holder." Basically, they can't assign you any type of duty at all is what they are trying to get across.
I agree that it's best to go with the most stringent interpretation.
An aside here: Guys, I hope you are treating this like I am; as a learning debate. This isn't a personal matter and nothing said here is meant to be offensive or as an affront against anyone (as far as I'm concerned or can tell).
I believe that this has been answered, as far as we should be concerned. I do wish I'd been able to find those letters, I had bad luck looking on the FAA website.
Anyway, the point at this stage is this: even if you find a less stringent interpretation, we've seen evidence that there is a fed who doesn't agree. Short of a letter of interpretation from the administrator specifically giving her blessing to doing CFI work and not counting it towards your 121/135 time, I believe that it would not be prudent to do so if you really want to be sure you are following the regs. That's not to say that you'll definately get caught if you do it... but do you really want to risk it?