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Drive flat tire onto/off of flatbed?

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Does the car display a message on the screen or emit an alarm when a tire is flat (or below may be 20 PSI ) ?
Owner's manual:

As an added safety feature, your vehicle has been equipped with a TPMS that displays a tire pressure telltale (Tire Pressure Warning) on the touchscreen when one or more of your tires is significantlyunder-inflated.Accordingly, when the Tire Pressure indicator light displays on the touchscreen to alert you about tire pressure, stop and check your tires as soon as possible, and inflatethem to the proper pressure (see Maintaining Tire Pressures on page 164). Driving on a significantlyunder-inflatedtire causes the tire to overheat and can lead to tire failure. Under-inflationalso reduces range efficiencyand tire tread life, and may affectthe vehicle's handling and stopping ability.
 
Owner's manual:

As an added safety feature, your vehicle has been equipped with a TPMS that displays a tire pressure telltale (Tire Pressure Warning) on the touchscreen when one or more of your tires is significantlyunder-inflated.Accordingly, when the Tire Pressure indicator light displays on the touchscreen to alert you about tire pressure, stop and check your tires as soon as possible, and inflatethem to the proper pressure (see Maintaining Tire Pressures on page 164). Driving on a significantlyunder-inflatedtire causes the tire to overheat and can lead to tire failure. Under-inflationalso reduces range efficiencyand tire tread life, and may affectthe vehicle's handling and stopping ability.
I was wondering what pressure value would trigger a warning?
 
I had a giant pothole rip the sidewall on two michelin tires before... Flatbed came... They drove the MDX onto the flatbad with two completely flat tires. I watched... It wasn't too bad. You are only driving like 10ft, going really slow.

As far as paying for someone to plug your tire... Discount Tire never charges for plugging a tire... I've taken lots of cars there to have their factory tires plugged.