That can only be achieve if the adapter has 3 antenna plugs and supports 3T3R MIMO streams. Note that per each antenna/stream, Wireless-N can carry 150Mbps on 64-QAM, 40 MHz channel connection while AC can do 433.3 Mbps on 80MHz channel width, 256-QAM. That's where the claim 3x the N speed comes.
If you looked at the teardown of the 2013 MBA, you'll see that there are only 2 antenna connections and the Broadcom Wi-Fi Adapter can only do 2T2R streams which effectively results to 866 Mbps connection.
On the same token, the maximum link speed on Wireless-N with 2T2R streams is 300Mbps.
Some of the 3T3R MIMO Wireless-AC adapters that can do 1.3 Gbps are only found on Desktop PCI-E x1 ports