Early command and control systems were considered secure through obscurity and lack of technical ability. Obviously, that isn't the case anymore. I don't know how old the drone design it, but considering that the US is saying all the technology on it is obsolete, then it's probably more than just a year or two old and could be controlled though the 'old school' technique. Now days, command links are encrypted to prevent the bad guys from even eaves dropping on the intel that comes down.
Spy satellites and spy planes don't have 24 hour coverage of the whole world, so they don't spend any time looking for something that they already control. Once they lost control, they no longer had a solid fix on its position. While I'm sure they would have scrambled to find it, finding a moving target of that size would be difficult at best and would take considerable time.
For things to go the way Iran suggests, the US would have had to have been flying over Iran for a long enough time for them to 1) intercept the command and control transmissions, 2) decipher the signals to determine what everything means, 3) design and build a system capable of mimicking the commands and displaying the correct return information, and 4) fielding the system to snatch the plane. The lack of any appreciable damage means they did an awesome job landing the plane, which would be VERY impressive from an untrained pilot. While not impossible, it would display a level of techincal capability that Iran doesn't seem to have.
Based on my experience, I think the most likely scenario is that the pilots lost contact with the plane after it had a serious malfunction. Then the plane wandered off is planned flight path, or even the emergency return path, and ended up crashing in Iran. It happens occasionally; the plane breaks hard and goes dumb. I suspect some sort of misinformation from the Iranians because I doubt they could have taken control of the plane and snatched it. I'd buy them disrupting the command and control links easily, but taking control is a couple orders of magnitude harder.