But now that you mention it pineteam, there is anecdotal evidence that some pilots in my company keep their ANR headset on during the cruise whilst their colleague is on speakers. This has become apparent during discussions regarding the use of personal ANR headsets on my company forum.
Now I don't like the idea of one pilot on headset whilst the other is on speaker but our company, unlike yours, doesn't prohibit it. What is more interesting though, in light of this discussion, is that none of these pilots mention interference. They are happy to fly for hours and hours with their ANR's on whilst their colleague is on the speaker with no hint of missed calls or other issues. Remember, this is in the cruise with the off side speaker wide open!
CRM-wise it must be a bit awkward, one on headset and one on speakers, hence the reference in your company manual. But again it goes to show that this interference is not universally felt/heard/noticed. Maybe it's a bit like the pressure waves some notice with ANR headsets. Most are not bothered, bot some are totally put off..