By law a contract is 6 months or less. I.e., the law provides for two types of residential contracts: two year (minimum) long term and 6 month (maximum) short-term, or temporary. Both contracts have different obligations to both lessee and lessor. Anyone who rents more than two consecutive 6 month rentals to the same person has the contract converted, by law, into a long-term 2 year contract with all the legal requirements involved, whether there is guarantee or not...
As far as a temporary rental requiring a DNI (because a CUIL or CUIT is required) from the person renting the apartment, that doesn't seem to be correct to me for obvious reasons, unless every renter is required to go get a CDI (because they can't get a DNI and therefore cannot have a CUIT or CUIL) just to rent an apartment. Of course, the government may make some regulation along those lines, without having thought things through, but my guess is that something was not understood correctly either by the journalist or by the listener if the answer was that the lessee themselves have to have a tax ID number to rent an apartment.
If this, for some reason, was the intent of this government to exclude foreigners (or make it very, very much more difficult to rent a temporary apartment), then I would say that this is a possible sign of things to come related to foreigners. But I highly, highly, doubt it.
Then, maybe they are referring to residents and citizens only that need to have a CUIT or CUIL to rent temporarily. Most of the South American expats from poorer countries who live and work here (residents, but not citizens), for example, living in pensiones (hoteles) may fall under this new regulation, but I don't know. In those cases, hotels or pensions are probably covered under another contract law of which I'm not familiar as short term stay (i.e., not temporary rentals) like any other hotel, except the residents there tend to live for months or years in their rooms. In that case, perhaps AFIP is trying to squeeze the owners of these places as well to fit longer-term stays into a temporary contractual situation and require them to have CUIT or CUIL registered.
The only reason I can see for a renter himself to have to be registered is if AFIP is trying to see that renters who should have X amount of income declared are paying more than they make for where they stay. For the people who live in pensiones or hoteles, that makes no sense because it would be like trying to get blood from a turnip and many of these people are fans of CFK anyway because of everything the government "does" for them. So that would leave expats from wealthier countries, but the amount is so small, and the quantity of people so small, that doesn't make sense either, to me.