Keep in mind I am filtering out sets and parts which doesn't leave me with a whole bunch of links.

Possible to sell more than 13 keys.

14 keys

http://www.tf2outpost.com/trade/14459827 - sold 13.5

http://www.tf2outpost.com/trade/14518036 - lets see how he does

http://tf2tp.com/trade.php?trade=9791632

http://www.tf2outpost.com/trade/14498521

http://www.tf2outpost.com/trade/14490628 - Multiple huntsmans (check ID)

http://www.tf2outpost.com/trade/14462972 - Offered Steaming Industrial (13-16)

http://www.tf2outpost.com/trade/14459827 - Offered Stormy Storm (~14) and was too late to accept 14 pure.

http://www.tf2outpost.com/trade/14371439 - sold 15 keys?

http://www.tf2outpost.com/trade/14423830 - declined offer Planets Mongolian (~14 keys)

http://www.tf2outpost.com/trade/14518544 - claims to been offered a steaming Gridirion (18 keys)

As you can see, very possible to sell for 14 keys, maybe even more

Feel free to counter / support my proof.