That is not the question. You already agreed that the police had cause to go to the TT because they had received a report of a suspicious man entering that theatre that was in the vicinity of the crime.
But the dispatch doesn't say "Have information a man acting suspiciously just went into the Texas Theatre". Rather it says "Have information
the suspect just went into the Texas Theatre".
No way would a description of a man in a brown shirt give rise to such a leaping-to-counterintuitive-conclusion dispatch
The question then becomes how they should respond. Now who are they looking for? A cop killing murderer who is armed and dangerous. Right? Maybe it turns out he is not the guy in the TT.
It would be very surprising indeed if some suspicious-acting brown-shirted guy in the TT should turn out to be the white-shirted suspect everyone's looking for.
However, change but one detail in the after-the-event Brewer story (---------->he described the man as white-shirted) and the DPD's response becomes perfectly intelligible. This
could reasonably be seen as "information
the suspect just went into the Texas Theatre".