score:2
Having appropriate travel health insurance is indeed one requirement for Schengen visas. Regarding documentation and the like, you don't need anything particularly mysterious but you should be able to show that you are coming for tourism (hotel confirmations, etc.) and have enough money to cover your stay. The things you mention in your question should be enough and that's probably what the people your friend talked to had in mind.
You should be asked to produce these documents when applying for a visa β if you need one β and you may be asked to show them again or provide other relevant information at the border if there are doubts about the purpose of your stay and that even if you don't need a visa (which is indeed the case for Chile). The logic behind this is that entry is conditioned on a particular purpose (e.g. tourism) and the border guards are supposed to check that.
Buying from a US agency, coming for the same tour, etc. is not directly relevant to the issue (just explain it if someone asks). The only thing is that it's good to have some confirmation of your booking and itinerary and a return ticket at hand to show you are really coming for tourism, just in case someone asks about it. Do send that your friend or have her print everything out in advance. As Chilean citizens have the same status than US citizens (annex II country), the US agency must be familiar with the requirements.
Formally, whether you have a visa or not, entry is never guaranteed and the border guards could refuse it and put you on the next flight back home (hence the scare stories) but if you are really coming for tourism and have all the necessary documentation, there is no reason you should encounter any trouble. Also, the Italians don't have the reputation of being the most difficult so I think you can relax and prepare to enjoy your holiday together.
Upvote:2
I would be rather curious about how your girlfriend would get deported if she can't enter without a visa.
There is a website Italian Foreign Ministry that allows applicants to determine whether or not they need a visa. And if you check on the site it will show that she will need to provide the proof of duration of stay. Basically usually referred to proof of onward travel (return ticket)
Upvote:3
When I was preparing tour to Europe (Schengen area), it seems that travel insurance proof is mandatory for visitor of my country (Singapore). However travel insurance is not that expensive (less than 30 USD), and at that time I just obtained it from any ATM in Singapore (it is not mandatory to buy it from a travel agency).
The tour agency should provide her with detail of itinerary (with her name and places she will stay in). However usually this kind of detail is only needed for visa approval. As long as she has the Schengen visa stamped in her passport and she does not doing anything against the law. There is no valid reason she is going to be deported.
Update : Just noticed thx to @Annoyed that Chile is in same annex II countries like Singapore, which means Singaporean and Chilean don't need visa to Schengen area. The border control did ask for proof of where are I was going to stay, so here is your tour itinerary comes handy. They also particularly checked the return flight ticket. They didn't mentioned anything about travel insurance.