[I'm applying the sysadmin privilage of making an exception to our usual no-military rule here, because the technical issues are sufficiently interesting].
Apply the usual skepticism about the claims, but there's something plausible in the following. As I understand it, the assertion is that Iran basically used radio jamming techniques to force the RQ-170 into RTL mode, then overrode the GPS signal with a fake one that made it think that "home" was an Iranian field.
An excerpt from the Christian Science Monitor, a good article that discusses what may have caused the capture:
Iran guided the CIA's "lost" stealth drone to an intact landing inside hostile territory by exploiting a navigational weakness long-known to the US military, according to an Iranian engineer now working on the captured drone's systems inside Iran.
Iranian electronic warfare specialists were able to cut off communications links of the American bat-wing RQ-170 Sentinel, says the engineer, who works for one of many Iranian miltiary and civilian teams currently trying to unravel the drone’s stealth and intelligence secrets, and who could not be named for his safety.
Using knowledge gleaned from previous downed American drones and a technique proudly claimed by Iranian commanders in September, the Iranian specialists then reconfigured the drone's GPS coordinates to make it land in Iran at what the drone thought was its actual home base in Afghanistan.
"GPS signals are weak and can be easily outpunched [overridden] by poorly controlled signals from television towers, devices such as laptops and MP3 players, or even mobile satellite services," Andrew Dempster, a professor from the University of New South Wales School of Surveying and Spatial Information Systems, told a March conference on GPS vulnerability in Australia.
"This is not only a significant hazard for military, industrial, and civilian transport and communication systems, but criminals have worked out how they can jam GPS," he says.
The US military has sought for years to fortify or find alternatives to the GPS system of satellites, which are used for both military and civilian purposes. In 2003, a “Vulnerability Assessment Team” at Los Alamos National Laboratory published research explaining how weak GPS signals were easily overwhelmed with a stronger local signal.
“A more pernicious attack involves feeding the GPS receiver fake GPS signals so that it believes it is located somewhere in space and time that it is not,” reads the Los Alamos report. “In a sophisticated spoofing attack, the adversary would send a false signal reporting the moving target’s true position and then gradually walk the target to a false position.”