Tbh, its one of the oldest scams in the book, and is becoming increasingly rare, but still happens. If I had a call like this, I either know whether ive paid the bill or not (its called keeping your finances in order), and I also know what landline phone company I am with (surprisingly, it says the name on each and every bill I recieve, I also specifically chose them, they have a stupid name, and most people wont have heard of them, but they are cheapest around for my particular needs because I do my homework when choosing utility providers lol).
If they told me they were working for a different company to the one I am with, and then proceeded to inform me that I had not paid my bill, id tell them to sue me and put the phone down, and if it were my phone company, and I knew I had paid my bill, id politely end the call and id contact my phone company myself to resolve the issue.
Simple rule with telephone calls is to NEVER give out any personal or financial information if the company cold-called you!! Always tell them you will telephone your respective company to resolve the issue, of course if you asked them to ring you back at a specific time, its different as thats not a cold-call, but quite simply, dont be STUPID.