Of course the police knowing the law makes it much better than a citizen taking the risk of saying, I think I might know the law but I’m not sure. Then it might lead to an illegal arrest and a lot of trouble for the citizen. It is not because the citizen cannot make the arrest but most citizens are not that clear on the law.
Any citizen has the authority in Texas to make an arrest for a felony or a breach of the peace that is witnessed by the citizen. Any peace officer has less restrictions and can arrest for any crime witnessed. That is where the statewide jurisdiction comes from. Technically citizens have a limited statewide jurisdiction.
So if a cop is out of his county and witnesses a crime other than a minor traffic violation, he can lawfully make the arrest.