One common exception to the rules of English grammar (and the rules of grammar in most other languages too!) is that orders or instructions do not have to obey the rules! The classic example would be a road sign that says "NO LEFT TURN". You wouldn't want a road sign to say "You cannot turn left here" - you'd have crashed your car before you'd finished reading it. Likewise, instructions, especially bullet-pointed steps are usually written in a slightly abbreviated form.
You were wrong to use the comma because saying "Confirm the message playback is not distorted" is essentially the same as saying "You should confirm that the message playback is not distorted". But your colleague's is not quite correct either. I think it should be:
Confirm the message playback over the loudspeaker is not distorted and that it is clear, with minimal noise from the recording. (note the comma)
Or, given that "clear" means the same as "not distorted" you could probably shorten it further. Also, if this is an instruction to be understood by all should you not clarify what "noise from the recording" means? Surely everything on a recording is "noise". I would probably write::
Confirm the message playback over the loudspeaker is clear and with minimal background noise.