It is not "secure" per say. The radio transmissions occurs at "thousands" of watts - from a foreign country. It is not hard to figure out, with the proper radio direction finding equipment, where the transmission is coming from - SUCH as using submarines - aircraft - satellites and "other methods".
Some codes have been "cracked" before. That is why the NSA and the CIA have all those mathmaticians.
When done at HF, as most numbers stations are, the message is absolutely secure. Sure, you can tell where the source is, but that is all that you can tell of a “one way secure voice link” (numbers station). Using propagation mapping and knowing time, frequency, and knowing or assessing power levels and antenna patterns, you can make predictions of the possible area of the intended recipient, but that is not realistically going to help much. You can tell the message was sent, but not whom the message was for, usefully where they are located, or what the message contains.
This is why, in the past, it was very common for numbers stations to actually be sent from national short wave broadcast facilities (and is still done so by the Cubans and Taiwanese). No one cares if you know where the message comes from, that in no way endangers the assets in the field or tells you the nature of the message contents.
While it is true many different types of codes have been cracked, when properly used a one time pad is uncrackable. Unless, of course, you get hold of the one time pad itself.
Not sure why that (and other) articles take the tone that numbers stations ever went away, or are even less active than in the past. Numbers stations still are heard many, many times a day. While some of the most famous are gone, new ones have taken their place, generally from other nations. In Europe, where the historically most active listeners are/where, the number of stations is reduced, but in Asia there are more than ever. And some of the stations have shifted to digital formats, so are less followed or less recognized. Numbers stations pre-date the Cold War, and they continue as a viable secure link today.
T!