While I mostly agree with you, the PD also has to enforce the law on the books.
I am going to deviate from the LIRR for a second to talk about another MTA agency, NYCTA Subways. Transit cops often write up summonses for violation of NYCTA Rules of Conduct Section 1050.9(c) which they
say bans photography. In fact, here is the actual text of the rule:
Photography, filming or video recording in any facility or conveyance is permitted except that ancillary equipment such as lights, reflectors or tripods may not be used. Members of the press holding valid identification issued by the New York City Police Department are hereby authorized to use necessary ancillary equipment. All photographic activity must be conducted in accordance with the provision of these Rules.
See, photography is legal on NYCTA Subways, yet cops decide to not read the books and enforce a non-existant rule. Now, if you do get a summons, you simply write a letter explaining the rule on the books, get it notarized, send it into TAB court, and they'll rip up your summons. But cops should not be enforcing laws that do not exist.
Going back to the LIRR, it's a very similar situation, except that the MTA Police cannot write you summonses. But they can tell you to stop. Now, the LIRR does not have a rules of conduct posted online, nor do I believe that they even have a full rules of conduct. But there is no rule that says that photography is illegal on the LIRR. Therefore, the MTA Cops have no right to bother us unless we are creating a potentially hazardous or dangerous condition.