The conflicting advice is confusing to sort out, because the logic seems to have got the cause-and-effect connections wrong. So let's start again...
The tires are the only part of the vehicle that is in contact with the road, and that contact has to support the weight of the vehicle.
The maths behind that are simple: weight supported by a wheel = (contact area of tire) x (tire pressure).
The contact area is critical for the vehicle handling. Too small, and it will tend to understeer, it will be easier to spin the wheels, and it will take less braking force to lock them. Too big, and the tire sidewalls will have to flex more as the tire rotates, which will overheat the tire.
So, the answer to your question is to find how much down force gets applied to the vehicle through the towing hitch, and then adjust the tire pressures to match that change and keep the contact area the same. Note that the downforce will affect the rear wheels more than the front, though it may actually reduce the download on the front wheels by trying to tip the vehicle's nose in the air - in which case you might need to reduce the front tire pressure. (But that is only likely to be the case if you are trying to exceed the vehicle's rated maximum towing capacity.)
Note, the down force change is not the same as the weight of the trailer being towed, assuming the hitch and drawbar are the right ones for the job. You may need to adjust the drawbar to "level" the trailer and get the recommended down load - the wrong value can make the trailer "snake" at high speeds, for example.
The vehicle handbook is the best source of the correct pressure changes, not "some guys on the internet." Getting it wrong could be life threatening!
As another answer said, you need to change the pressures when you hook up the trailer and restore them as soon as you are done. Don't drive the vehicle for long distances or at high speed with the wrong pressures when not towing!