Wow, I finally got a discussion started. Thank you folks.
A bit more inspection of the device shows that it really can power an Arduino, but there are things that concern me. First, it does have a top voltage limit (open circuit) that falls within the range an Arduino can handle as well as a current limit that, when exceeded, shut it down. It doesn't taper off, it just quits. The killer though is that it is very noisy. I don't have a scope so I can't paint you a picture of the noise, but measuring voltage through various capacitors to block the DC shows a substantial noise or ripple coming out of the supply. Comparing that to an apple two board wall wart ( one of the 1 inch cubes ) the apple one has almost no noise at all and the CC supply has a ton. This noise wouldn't make any difference to an LED, but it could to a more complex device, and it appears the Arduino has enough filtering on board to work. This may not be true of something that I threw together in the garage one evening.
I can't tell you what the chips are that it uses, the markings are blurred or missing on almost every part; the inductor has rings, but I can't tell exactly what colors they are. You've all seen this before.
Regarding the size, the two CC supplies I have are about 3/4" x 1/2" x 1/2", and I got two of them under 5 bucks, so you see why they are appealing as a possibility. Remember, the link I posted was just the first one I hit on ebay, that may have been a mistake since several folk grabbed on that as a negative. The point was that these CC devices are incredibly easy to find and don't cost much, which only a couple of people noticed. Tiny little constant voltage supplies that run off wall power are not anywhere as numerous or cheap. I venture to say that you'll find 10 or so CC led supplies or more for each little CV supply and they'll cost substantially more (not counting getting a usb charger and gutting it).
In answer to the various comments about the apple chargers ( 1" cubes ) the one I have torn apart provides a constant 5.1 volts regardless of the state of the battery in the device it's hooked to. If I hook it to a resistor and force it past the rating of 1A by lowering the resistance, it drops below the 5V level until it reaches some point where it shuts off. That's usually just after the resistor burns a blister on my hand. This little device lists a ton of certifications on the bottom in print so small I have to get the big magnifier out to read it. So, it appears that something in the device with the battery helps the charge cycle along somehow. I don't own a single apple device to look at to see; I probably wouldn't pull an expensive device apart to check either.
See, I don't just discount a possibility simply because it doesn't have the right name; I want to actually see if it will work or not. Bouncing it off other folks helps fill in the gaps that I don't think of or understand (yet). That's why I asked for your thoughts in the very first post.
Your various comments led me to check for noise in the output, so I don't think this particular kind of device is the answer to my need for a tiny power supply, even if it was a compelling possibility.