Are Electronic Dog Doors Safe?

I was looking for electronic dog doors for a rather large dog and I came across something rather disturbing. Your mileage may vary.

I realized that the bigger dog doors are sized about 20″ by 14″, enough for a small human to slide through. And what opens this door is a sensor attached to dog collar which opens the door when the dog is nearby.

The door can be activated from upto 5 feet away and can remain open upto 5 seconds.

It appears to me very plausible for someone to appropriate the sensor from a dog (or maybe even fabricate one) and use it to break-in.

I did some googling and found that electronic dog doors are actually recommended in response to burglary concern:

Question: I would like to install a doggy door in my laundry-room exterior door. I have a mid-sized dog and I am concerned that a burglar could crawl through the dog-door opening, not to mention unwanted animals. Is there any alternative to a doggy door that would allow my dog to enter and exit my house without worrying about undesirables doing the same thing?

Answer: You should purchase an electronic pet door. This state-of-the-art mini door is activated by a directional sensing system located on your pet’s collar. The signal emitted from the collar not only tells the door how far away your pet is, it informs the door in which direction your pet is travelling. This means that the doggy door will open only when your pet is approaching, not when he is just wandering, sitting, or sleeping nearby.

Have you had any incident or heard any stories about burglary using large electronic dog doors?
What are the alternatives (other than opening and closing the door each time)? I wish there was some implantable sensor chip.