The BA stuff is clearly rubbish, as I personally know an Airbus TRI/TRE there who is 6'6. I have not flown the Airbus but he tells me it's significantly more comfortable for a day's flying than the 737 for a tall man.
I really find it difficult to understand why CTC have told you that, unless it's a restriction in any of their aircraft, or like the RAF they use it as yet another way to screen out candidates.