The OP. Those people Musk interviewed are "the US authorities".
But who are those people? What were their job titles, which agency did they represent, and were they actually representatives of said agencies or were they just random people that Cowboy Rocket found?
If you would bother to listen to about the first 2 or 3 minutes you know one of them was congressman of that district and the others were sheriffs or some other official law enforcement job for that geography.
I would rather not give Elon even 2 minutes of my time, but it appears (as Patooka said) that you are basing your opinion that the border is utterly undefended and anyone is free to cross at any time on the word of a very unreliable source (the aforementioned wannabe cowboy) who "interviewed" a (and I'm guessing here) Republican Congressman and a couple of (again, wild guess) Republican Sheriffs who are hardly objective. As for them being "the authorities," it has apparently escaped your notice that the responsibility for patrolling/controlling access to the border is not "a few local politicians in a very small town in Texas" but rather the federal government - specifically DHS - and as such a reasonable person would consider them to be the source of authority.
It also appears that lonesome wrangler Musk went to just one particular area near one particular town along the border, and he (and you) are judging the entirety of the thousands of miles of the US/Mexico border (or is it "boarder?") on that one narrow - and again, biased - data point. Some dudes who are mad at Joe Biden say so, and therefore you believe that the border is utterly undefended and I could easily load up a truckload of cartel members carrying AK-47s and drive them right across the border at the Santa Teresa, NM port of entry and nobody would even try to stop us.
If choosing that one crossing seems oddly specific, it's because I know it well...having lived in Santa Teresa right up the road from that port of entry. You bring with you Pardner Elon and his Texas deputies from one bit of land, and that's nice, but I have some experience here as well. Over the past 30 years I have lived in 3 border states within varying distances from the border, and have also crossed that border back and forth so many times I've lost count. I used to go to Mexico once or twice a week for a few years.
Now, are there problems along the border? Yes. You head from downtown El Paso to Santa Teresa along Paisano Drive and you get a real close up look for yourself. Back in the day it was less than wise to go there at night, but I never ran into any problems. Is the border a free-for-all like you and Vaquero El Musko make it out to be? No. It is complex, but you're trying to both over-simplify it and fear-monger at the same time. With your source being some guy who fancies himself a dude and just happens to own a social media platform, and this leads you to believe he's an objective fountain of truth and also an expert on border policy because....you watched a video?
And you expect others to watch a few minutes and agree with you that the entire population of the world is gathering in Mexico to stream into the US while CBP sits back and says "nothing we can do here"?