Hi. I am in the process of finding my "door to door" package as we speak. Unlike your topic, I had my parents put everything in a box and ship from a standard USPS local store to my address in Pilar. (There isn't a tracking number on standard package shipments...as in they don't even offer it).
Short version: Yes, I got the box, yes they followed the rules. No they didn't steal my box! If you learn the bureaucracy, it works.
I found that there are two different paths here. Public mail and Private couriers. I found this article to be very helpful and very very true. http://www.lanacion.com.ar/1932079-guia-para-entender-como-es-el-puerta-a-puerta
Here is the number for correo central. 01148919191 They answered me after about 10 minutes waiting. They were very kind and patient.
For both options, you'll have to deal with the AFIP at some point. You'll have to have a "clave fiscal" (you need a CUIT/CUIL/CDI and you need to go to AFIP to get this in person). IF you can't obtain this clave fiscal, you need to have the box come in the name of someone who can do all this for you. Tell them you want this to for "una encomienda puerta a puerta" so that they do your digital fingerprints and give you "level 3" access.
You'll have to get familiar with these lovely steps:
http://www.afip.gov.ar/guia/documentos/PAPEnviosInternacionales.pdf
Private mail:
I assume Amazon will use a private courier, like Fedex with partners with other local couriers further into the country or DHL which goes almost anywhere. My bet is that you won't have a choice of the courier Amazon uses but that it will likely be private. You have up to 5 shipments a year, which can be up to 50kilos and 1,000 dollars (each one).
The DHL courier (which I have used outbound for docs and boxes) will take care of MOST of the paperwork. Which is a blessing. The only thing you'll have to do is for a box you receive here, is confirm that you received the box. On the AFIP page once you sign in, you go to "declaración de envíos postales internacionales" and will have to "confirm" the receipt of the box. There is this (rather 2005 looking) system that the AFIP uses to fill out custom forms -- Sistema Informatica Malvina. These forms you aren't supposed to have to do. BUT, once you receive the box, you are supposed to go into that same system and confirm you received it. The difference here is that public mail makes you fill out the forms, then confirm it. Private takes care of this for you (they are supposed to anyway).
Here is number for the Sistema Informatica Malvina (the system the AFIP uses to manage shipments and taxes): 01143473974
Public mail:
I WISH my parents had the extra bills to think about the private courier, but alas, they are cheap. Here is my current experience. You can receive as MANY shipments a year as you want.
Watch this video for correo argentina It has 3 options (look at the headers/tabs) and each are helpful. http://www.correoargentino.com.ar/puerta-a-puerta/
You can get as many boxes as you want. Unlimited. (There are more rules I can't recall about limits to have many # of the same items you can have, like you can't have 20 sunglasses, etc. Because you'll be like a reseller in disguise.)
If your box is UNDER 2 kilos AND UNDER $200 USD it will come to your house, eventually.
If your box is OVER 2 kilos OR OVER $200 USD it will stay in the aduana no matter what. You'll have to go get it.
It's important to know that you have $25 you are allowed ONCE a year (so kind right). Even though you are allowed to receive up to $200 in each box, you will pay more. For example, if your box is worth (value or objects, not taxes) $50 and you haven't used up your $25 yearly allowance, you'll do this math $50-$25 = $25 is what you will be taxed on. You'll be taxed on the items differently, but it can't be more than the 50% value you would be slammed with at the airport. So at the most, it would be 50% of the $25 you surpassed. You'd pay an estimated $37.5 USD (value in USD transferred to pesos).
You'll receive a notice from the mailman that you have a telegram. You go get the telegram. It gives you instructions.
If your box is under the limit, you'll be told to go to the AFIP, and complete the forms. You'll be given a long (18 character I think) alphanumeric string which is a tracking number for your box. In addition to whatever value they determine you need to be taxed on, you'll pay $100 pesos more for "administrative and storage fees" (we really know its 100 pesos for shipping it again to your house). That AFIP system will generate a voucher for you with a desc of items, an amount to pay and a barcode. You have 1 day (that same day!) to take the VEP (volante electronico de pago) to the Pago mis Cuentas or Banelco and pay this amount. After that, you regenerate the same page with a new barcode.
If your box is over the limit of weight/amount you get a request to go to the aduana directly to pick it up and what fees you'll have to pay. You'll be assigned a small alphanumeric string to identify your box. You'll be told to go to the AFIP as well. and complete the forms (and pay the money). You have 30 days to get it from the date you receive the telegram!
So, In my local mail experience I had a 3.5 kilo box sent, under $25 un value. I declared it was $15 total on my forms. I didn't pay anything and did not have the option to send it to my local post office or house, but I have to go pick it up in person at retiro. Notice, I also didn't get a "VEP" form generated. The system just marked my box as "paid and liberated"...but after investigating I just need to take my form down to the aduana. And that's it.