No, if they crossed the border illegally whether by accident or on purpose a border patrol agent that responds has no choice but to detain them. We are law enforcement officers not judges.
If an agent did not detain someone for illegally crossing that agent would be placed under investigation. I have caught illegals a few feet from the border and they sometimes ask if I can just let them go back. The answer is always no.
I was in Derby Line VT this summer and had an interesting talk with an officer who was parked on a road that crosses the border.
In Derby Line, many streets cross into Canada, but most of them have been blocked, it looks like recently. One road crosses a small creek on a bridge and then climbs up a hill to Main Street, where there is a Border Patrol station where people are supposed to check in.
Before 1910, it was legal to build on the border, and the town library has entrances in Canada and in the USA. In the library, there’s a black line on the floor with a small US/Canadian flag display that marks the border.
When you are there in what is basically a peaceful little New England town, you would imagine there’s not much for CBP to do, but you would be wrong.
People who can not get permission to enter the US, or who find it easier to enter Canada with contraband than to get through a US airport, have a confederate drive them to the Canadian entrance to the library.
They go upstairs and browse for a bit. They get a text, walk out the US door, a car pulls up for a 1.5 second stop, and in 90 seconds they are on I-91 heading South.
If you stop in your car in front of, or near, the library to admire the architecture, expect a chat with Border Patrol within a very brief time.
On the other hand, I took pictures of all my kids with one foot in Canada and one foot in the USA in front of a CBP officer with no hassles.
White privilege, I suppose.