when black plays contact, white gets stronger  

Take this example. looks heavy. A play at a is more likely. (We do not know the surroundings, so may be OK.)

Thick, but  

White might play this way. (Again, depending upon the surroundings.) Now you may say, White has become thick. To which you get the reply, But look at Black's territory!

Rather than trying to prove anything, maybe showing some pro examples would be good. Alternatively, find some DDK examples of where attaching did not work out, or should not have.