Federal banking regulator here. In order of likelihood, here is what may have happened:
Error made by a credit bureau if it's only on one report. If it's on all three, it would be an error by Wells. Either situation would be common.
You may have done business with Wells at one point without being aware of it. They finance cell phone contracts, furniture purchases, auto purchases, ad infinitum ad nauseum, and you may have made payments to a servicer that passed through to Wells. In that case, a Wells associate may have found your info internally, slammed you into a card, falsified some charges, reversed the charges, and closed the account. They would have kept it open only long enough to meet the particular requirements of the incentive plan.
Your identity was actually stolen and used to open a new card.
None of these scenarios would surprise me. I know the Wells situation really well, and their incentive program was totally fucked. Combine that with a lack of basic controls, and what happened was totally predictable. Associates were (mostly) trying not to get fired for failing to meet absurd sales targets. Not an excuse, but the avarice was mostly at the higher levels, not at the customer-facing level.
The error situation is most likely simply because errors are so common. Not because Wells didn't screw people, because they most certainly did.
Get all 3 major credit reports. Contact Wells' ethics hotline. Should be easy to find now because they are under a Consent Order which requires a high level of responsiveness. No matter what happened, get it off your credit report and chase down answers to your satisfaction. If you aren't happy, go to helpwithmybank.gov and put in written complaints and call their primary regulator (OCC - Office of the Comptroller of the Currency).