Hales fell for six on the first day when he clipped Mohammad Amir off his pads and was caught by Yasir Shah, diving forward, to leave England 23 for one.
Hales stood his ground, believing the ball had not carried to the fielder.
Umpires Bruce Oxenford and Marais Erasmus called on television official Joel Wilson for assistance.
But with available replays inconclusive, the West Indian felt there was not enough evidence to overturn his on-field colleagues’ original ‘soft signal’ of out.
Hales walked off shaking his head — enough in itself to risk action for showing dissent at an umpire’s decision — and England were 23 for one.
At the time, Daily Mirror cricket correspondent Dean Wilson tweeted: “THAT IS OUT – Hales (6) clips Amir to Yasir at mid-wkt who takes a low catch diving forward. Replays are unclear but umps say out. 23-1.”
But after close of play, Broad — the son of former England opener turned match referee Chris Broad — replied: “@CricketMirror replays are unclear? You don’t believe that do you?”
Hales, above a screen grab of the incident that appeared to show the ball touching the grass before Shah claimed the catch, added: “@[email protected] bit blurry to be fair!”
That comment might be interpreted as being mockingly ironic of the umpires, rather than supportive of the officials.
Either way, both Hales and Nottinghamshire team-mate Broad had exposed themselves to the possibility a fine or even more severe punishment from match referee Richie Richardson, the former West Indies captain.
Pakistan ended the day three for one in reply to England’s first innings 328, a deficit of 325 runs. England lead the four-match series 2-1.