According to a report in Motherboard, there's a secretive air freight business running in an old DHL facility in Wilmington. It's impossible to say who is behind it, but as Kari Paul explains, Amazon would be a safe bet.
The facility in question is Wilmington Air Park, a cargo airport in Ohio that was used by DHL up until 2008. At that time, the company announced it was abandoning the operation, cutting 7500 jobs, and leaving two runways and all sorts of warehouse space empty.
Starting in September, a new tenant took up residence. Under the name of Air Transport Services Group, it's been operating four flights a day to four different airports, using a few leased Boeing 767s. The airports it's flying to — Allentown, PA, Ontario, CA, Tampa and Oakland (OAK) — all have Amazon distribution facilities within 97km, although that's not saying much, given Amazon has 75 centres across the US, near basically every major population centre.
Motherboard also quotes a few other sources, from staff at the airport to industry experts. Amazon, for its part, neither confirmed nor denied the allegations.
It's a very plausible rumour: Amazon is a logistics company that would probably be quite adept at running its own shipping, or at least a small part of it. It also has a reputation for limited trials of programs that don't always work out. This would certainly be cheaper than making another dud smartphone; whether it works out more successful is a different question.