You're probably right, I bought them on eBay and they were rated 1/2W. I computed the current at around 700ma and decided it was sufficient for my needs, probably times ten.
Here's a lower rated one on Digikey, 560ma and 740mOhm resistance. The B78108S1223K is smaller in physical size than my choke, using it's specifications, I come up with a power dissipation of .23 watts. Given the size of my part, the 1/2W rating makes sense to me. I put one on the bench and cranked up my bench supply to .7A. current limit, the part was dropping about .55 volts and the temperature went from 21C to 38C in three or four minutes. It seems it easily handles the .7 amps without breaking a sweat.
However, there's no magic here, consider the choke as a low value resistor as far as 60hz is concerned, it's just dissipating a little bit of current. A 1/2 ohm resistor would do the same in the circuit, and probably get about the same temperature.
The "magic" of the choke is at RF frequencies, it has a much higher reactance. For 22uh at DCS frequencies, that's 452 ohms, hence my use of it to block the 3.27mhz DCS signal. At 60hz, it's reactance is 0.0083 ohms, in other words, it's purely the DC resistance of the windings that determine it's characteristics.
