Then they'd have to be stealth airplanes and unwilling to communicate with the patrol. From the source [1] article:

Shortly thereafter, the pilot contacted two radar stations - one close by on the coast, and the other the main DGAC Control system (Ground Primary Radar) in Santiago - to report the unknown traffic. Neither station could detect it on radar, although both easily picked up the helicopter. (The object was well within the range of radar detection.) Air traffic controllers confirmed that no traffic, either civilian or military, had been reported in the area, and that no aircraft had been authorized to fly in the controlled air space where the object was located. The on-board radar was also unable to detect the object and the camera’s radar could not lock onto it.

The pilot tried several times to communicate with the UAP, using the multi-national, civilian bandwidth designed for this purpose. He received no reply.

[1] http://www.huffingtonpost.com/entry/groundbreaking-ufo-video...

1. https://theaviationist.com/2017/01/02/in-1986-u-s-president-...

You have to switch between frequencies in order to listen and communicate, and there's a toggle that allows you to do this. If you're not tuned to the correct frequency for the airspace you're in, then you're not going to hear any commands from the controllers for your airspace.

It's entirely possible that it was an international flight with a radio not tuned for the correct frequency for the airspace.

What kind of airplanes have you seen with radios that can listen on several frequencies at the same time? Are they large commercial craft?

Some early Junkers maybe?

Of course, it's unsurprising that a government committee for investigating UFOs didn't bother to do any due diligence like actually checking publicly documented flight paths. You don't get continued funding if you undermine the purpose of the position. (The article reports their claim that there were no planes in the area to be seen, but there were in fact three.)