I know this will sound silly, but I am thinking towards a few simple things such as:
[*]Is there a Mirror which may possibly be reflecting Infrared Light towards the PIR sensor?,
[*]Is the PIR sensor aimed directly towards a window for this room?,
[*]Is the sensor Tweeked to the limits - such as highest sensitivity and farthest range,
[*]Could the lady be scarring a Cat when she turns on the light - thus making the Cat run away?,
[*]Could the lady simply not realise that the PIR controlled lights were on before she turned on the others?
[*]Could the Wind be responsible for false triggering the PIR sensor? - like blowing trees / leaves and reflecting Infrared light.
[*]Have Mulder and Scully been called out to check into this yet?...had to throw that one out!
If these simple methods do not yield results, try analysing the circuit[s], then call for an exorcist