Have you checked to see if the "DTC" ( Diagnostic Trouble Code )
for TPMS Sensor Low Battery is present ?
( Press and hold both the Scroll UP and the "
i" buttons while switching on the Ignition.
Keep the buttons pressed in until the Speedo and Tacho needles have finished their sweep,
when the Diagnostics screen should be displayed with any stored DTC's.
( Use the Scroll buttons to see if there is more than one DTC stored ).
The Code is L0001 for the Front sensor, and L0002 for the Rear sensor.
If those Codes are not present, then I don't see how the Dealer can advise the Battery is Low ?
I don't know for sure, but I guess that if the Sensor had beeen damaged,
it would exhibit the same symptoms as a completely flat battery,
with NO Pressure reading displayed, the red TPMS Warning light ON,
and the TPMS Symbol flashing, but a completely flat battery
would have beeen preceeded by repeated LOW BATTERY warnings
over a period of time, so if you have never seen those messages,
and the TPMS Low Battery DTC's are not stored, then it is reasonable
to assume that the Sensor has failed, or has been damaged.
After checking for those DTC's, if they are not present,
I would consider asking the Dealer that fitted the tyres to allow you to be present
when the tyre is removed, so that you can see for yourself if there is any obvious damage,
and take things from there, explaining that even if there is no visible damage,
the system was working properly with no LOW BATTERY Messages prior to them working on it.
Cheers

