You’re not wrong, but the way you put it makes it sound a little bit too intentional, I think. It’s not like the camera sees infrared light and makes a deliberate choice to display it as purple. The camera sensor has red, green and blue pixels, and it just so happens that these pixels are receptive to a wider range of the light spectrum than the human eye equivalent, including some infrared. Infrared light apparently triggers the pixels in roughly the same way that purple light does, and the sensor can’t distinguish between infrared light and light that actually appears purple to humans, so that’s why it shows up like that. It’s just an accidental byproduct of how camera sensors work, and the budgetary decision to not include an infrared filter in the lens to prevent it from happening.