Since it had a gag order, she likely wouldn't have been allowed to tell him. The government doesn't care about the security implications of these backdoors, they just want the data.

Also, Yahoo spent many years fighting similar requests (I think before anyone else did) and won nothing.

She also was obviously being advised by Ron Bell, the GC. If she didn't tell Stamos, it was probably based on the guidance of Mr. Bell. I'm not sure we can fault Mayer much on this one.