Possible scam

for a number of weeks this company appeared on our caller ID without any message.  When we returned from a trip, we had a recorded message from them, saying that if we were not the person they were trying to contact, please hang up.   I called the phone company to see if the person mentioned had ever had our number,as we moved to this area five months ago.  I was told that the name would not appear unless it was an account with an outstanding balance, and such was not the case. The advice was to ignore the recording.    Immediately after I spoke  with the phone company, the phone rang and it was Asset Acceptance.  Their recording asked me that if I was not the person they were looking for, to press 4 and remain on the line to talk with their customer service people.  I did so, and then began to be worried that it was a scam, and that I had inadvertently fallen into their database, so I hung up.      I see from the internet, that there are cases in which people have been scammed this way by a company claiming to be Asset Acceptance, or by unscrupulous employees.