Final answer:
The statement could be true under certain circumstances where the police officer has reasonable and probable grounds for an arrest without a warrant, as recognized by the Fourth Amendment and clarified in Terry v. Ohio. It's important to consider local laws that may vary in detail regarding the arrest for trespassing without a warrant.
Step-by-step explanation:
In regards to the statement that a police officer or the occupier of a premises, or a person authorized by the occupier, may arrest without a warrant any person they believe on reasonable and probable grounds to be on the premises in contravention of section 2 of the trespass to property act, it's crucial to understand the legal standards for arrests and searches without a warrant. The Fourth Amendment protects individuals against unreasonable searches and seizures and states that no warrants shall issue but upon probable cause. Despite this, specific circumstances allow law enforcement officers to act without a warrant. For instance, in Terry v. Ohio, it was established that police may stop and frisk a person if they have a reasonable suspicion of criminal activity.
However, the details of such laws can differ by state and by country. Without a warrant, an officer's ability to arrest someone on private property for trespassing depends on whether the officer has reasonable and probable grounds to believe that person is committing an act in contravention to the act mentioned, such as the trespass to property act.
Therefore, granted that the officer has such grounds, the statement can be considered true, but this would be heavily dependent on the specific legal context within the jurisdiction in question. It's essential to consult the local laws or a legal expert for accurate information related to a particular location.