Hi Innerzone and Fern. What likely happened here is that the person who called you, accusing you of calling them, received a robocall. The robocall likely showed your phone number in their caller ID. Obviously, the robocall did not come from your actual phone, but they found a way to make it look like it did. The whole purpose is for the robocall to appear as if it was from a local number in your area (as opposed to half across the country or even abroad). That makes the person more likely to pick up the robocall, which is what the criminals that do the robocalls want. Even if the person does not pick up the call when it is ringing, the call (showing your number) will likely appear in their "missed call" records. So they might call YOUR number and thus the confusion/anger.

I've had the same situation happen and the person told ME to report the robocall, since he received a call seemingly from my phone number. That does no good, and I told him as much. The only real solution to stopping these criminal robocallers from doing this, is to complain about it to your congressman/woman. Further laws must be passed and pressure put on phone companies. that help prevent this from happening. You might think that it would be a no-brainer, but many politicians are not eager to force things on corporate America or make things difficult (or less profitable). This is partially because of some politicians' view that government should not be too involved, and partially because some politicians ultimately get money from supporting corporate interests (from both major political parties).

The article below may explain this robocall situation better than me:

Phone Companies Can Filter Out Robocalls, They Just Aren’t Doing It