I've been busy with a phone charger (and did a failed kickstarter for that... that's another story) and yes, what they do is probably legit and also yes, it is probably going to break some chargers and overload usb ports.
They almost definitely have something like a TPS2543 or similar CDP controller inside which engages with the button. That scans the downstream device for compatible charging methods and manipulates the voltage levels on the D+/D- ports in accordance with whatever the phone/tablet recognizes. There are quite a lot of these chips around, they are cheap and they work very well. One size fits all designs, really.
They bank on the assumption that:
1) The PMICs inside phones and tablets aren't dumb, they don't just start drawing 1A when they are told they can. They will do a scan of the power source, often in steps of 50 or 100mA, very rapidly and measure the voltage drop. They generally take either the externally programmed max current (in this case 1A), a lower current because the battery is already mostly full or whatever current corresponds to a preprogrammed voltage drop. For instance, my Galaxy Note 2 scans in 50mA steps during half a second and settles on a current corresponding to a voltage drop of 200mV.
2) Polyfuses on USB ports in computers and peripherals (e.g. monitors) are never actively current limiting and have very large margins. A 1A polyfuse is guaranteed to indefinitely pass through 1A. It won't even blow at 2A, usually. Certainly not for the relatively limited amount of time that a large current is actually drawn.
This is all fine for >90% of boards, but you WILL get compatibility problems. A couple of hub controllers actually do implement active current monitoring (especially USB 3.0 and 3.1 stuff), and will just cut off current when they see anything on a logically empty port drawing more than 250mA. This is a growing problem for the future as we go to more well-managed peripheral interfaces! Also, as mentioned before lots of laptops have low-current load switches on the USB ports which means you can permanently damage a USB port if you draw more than 500mA from it (the load switch will just fry).
All in all; the product is probably legit and by the looks of it it's very likely just something they bought in wholesale from China as an existing product. They're making an absolute killing on margins. It's not bullshit as far as I can tell. Especially because they have thunderbolt support I highly doubt they actually have in-house electronic design.