you say the alarm said "off" but it sounded.
Do you mean the alarm panel was unset?
Did the control panel show an alarm status? What does the log say? Or did the wall siren go off without the control panel recording an activation?
If you have a bad sensor, it still has Tamper protection, so if, say, the lid was loose, or the spring not pressed tightly, you would have a tamper alarm even if the panel is not set. Taking the batteries out will prevent this sensor from triggering. You can also use "remove device" to prevent the control panel recognising its signal.
if the alarm is old (a 3500 is) then the battery terminals would benefit from being scrubbed with a nylon toothbrush and the merest hint of WD40. Duracell batteries are a non-standard shape and may not be the best choice.
The stories of RF interference with Yale alarms are commonly trotted out, but actual RF interference is not.
edit
I just checked my HSA3500 instructions.
They say:
"Tamper and low battery display
The control unit will identify the device
triggering a tamper alarm or low battery warning
when disarmed. The display can be cleared when
disarmed by entering PIN code, OK, and exiting
the Arm Home display by pressing [picture of return button]"