Can an OBDII scanner consistently return the wrong code?

A few weeks ago I had my 2000 Ford Taurus serviced in response to a P0171 code (System Too Lean). They replaced the MAF sensor and PCV valve which fixed the problem.

The check engine light came back after a week, so I took the car back in. They read it but claimed it was a P0460, told me it was a $900 part (not counting labor) to fix, but recommended that I not repair it because of the car's age/worth.

The same P0171 code came back yet again a few days later. Now I don't know whether or not I can trust my code readers. Is it reasonable to assume that both of my (cheap) readers are getting the wrong code?

Clear all of the codes and see if any comes back.
To your question. A reader is a reader, both should read the same codes off the car's computer. The better reader just can do more stuff.

http://www.obd-codes.com/p0171

The on-board and the reader communicate via UART, it's virtually impossible to read a code wrong (it would get a parity error if the transmission somehow got corrupted.)

But that said, you know the ancient acro GIGO, right? The integrity of the code[s] is mostly a feature of the numerous sensors providing input. The more anomalies there are in a given moment, the more exponentially complex the diagnostic logic tree grows. That's why they always want to clear all the codes and see what comes up first, to give the simple CPUs of 14 years ago a better chance at returning a salient conclusion.

Lastly consider that engine problems (particularly sensor failures) are often intermittent, they may be exacerbated by the engine being hot or cold -- 14 years on the highway is a long way from the lab where they develop and test those embedded systems.

I sort of wonder if mechanics nowadays sometimes follow those diag codes like the people that follow their GPS onto train tracks, and die there because they've forgotten how to think critically. Back in the day the mechanic *always* got behind the wheel so s/he could feel how it was running. Anymore they just want someone else to drive it until the check engine light comes on… I fear something [perhaps important] has been trampled upon by the relentless march of technology.

Code readers never give the wrong code. But shop routinely think they fixed the problem only to have it return. Your shop obviously didn't fix the root problem.