My guess is that by "isolate" the parent means it would be awkward to have others at the table hear that you are doing that (edit: asking for a phone number) or it might make someone who wasn't picked feel uncomfortable or even the person you've picked might feel uncomfortable in front of others rejecting (or even accepting) a phone number request.
My guess is that by "isolate" the parent means it would be awkward to have others at the table hear that you are doing that (edit: asking for a phone number) or it might make someone who wasn't picked feel uncomfortable or even the person you've picked might feel uncomfortable in front of others rejecting (or even accepting) a phone number request.