Totally agree that complaining on the air is inappropriate. The person concerned should have waited until om the ground and if so concerned then called ATC to discuss.
That said EATs are most definitely NOT regarded as estimates in the sense that we assume they can only get better i.e they are worstcase. Whil occasionally something may force EATs to be adjusted ti a longer time the fact is that in line with CAA approved procedures many pilots find it necessary to commit to LHR and do do on the basis of an EAT. Hence this person's concern
Doesn't justify berating on the airwaves though.
Regards
Diesel