They are so unorganized in Argentina I doubt anyone that is not Argentine has to worry about it! They have a tough enough time getting their own citizens to pay. I wouldn't worry about anything else. I am fortunate that I did my DNI several years ago. I just use my rental income on my property. I don't plan on declaring any of my assets in the USA and not worried about Argentina trying to find out.And even if you're not a legal resident in the US, if you spend most of your time there you are automatically a tax resident. That's how they were planning to use IRS records to find out who's living there (illegally).
I'm sure Argentina would have a similar rule about tax residency. In case the ARCA decides to examine and go after this one day, it won't mean that they will be exempt from taxes just because they didn't get a DNI.