That is absolutely not true. You need to study some history of the Southwest. Prior to the Mexican War there were constant skirmishes along the border leading up to the war breaking out. For many years there were military forts all along the Mexican border and troops regularly patrolled the border. The first Border Patrol was made up mostly of Texas Rangers and they were very serious about securing the border. All through the History of the US there has been border enforcement of one type or another and at times immigration and other illegal activities has gotten out of hand and it has been followed up by a crackdown.
Prior to the Mexican War the US had NO border with Mexico.
Any skirmishes would have been between Texans and Mexicans.
I was not speaking of Texas Rangers on patrol from time to time either.
Forts along the border and troops patrolling it would have been for use against the Indians not the Mexicans since the only raids by Mexicans was Pancho Villas' during the Mexican Revolution. Often the troops were to prevent Indian raiding parties from escaping back INTO Mexico.