Don’t show me on other profiles

I seem to have found the solution. The key was in my Google Contacts.

Apparently, because I'd added this person's Google+ profile it also created a contact under my "other" contacts. A quick search on part of his name revealed the two entries. I simply used the Google Contacts "Merge Duplicates" feature, waited a little while for everything to get in sync, et voilà! No more duplicate.

(In fact, the "Other Contacts" section is filled with people whom I have added to Circles in Google+.)

These contacts are apparently separate from the ones added by Google+. If I use the find duplicates feature to merge them, will their phone numbers now be associated with their Google+ profiles in Google's databases? Will this information be visible to other people? In short, will this violate my friends' privacy?

No, it depends on their privacy settings.

I seem to remember some scare where Facebook might or might not have grabbed phone numbers and associated them with Facebook profiles by picking them out of friends' phonebooks on their smartphones.)

That wasn't a scare, neither were the numbers "picked up", it was opt-in.