Is iphone5 a true international phone

I'm a total cell phone newbie; esp when it comes to the latest smart phones. I've been thinking of upgrading my older Verizon cell phone (I have basic Verizon cell phone service now, in rural SC) to one that could be used on 4G locally and also internationally when I go to Europe next summer. I need to be able to send and receive text messages to/from my wife, and also to be able to call from some place in Europe to some other place in Europe occasionally. I also want to be able to go online and check email, maybe use a train timetable app once in a while, etc.

I know what it means to buy a "quad band unlocked" phone. I know that I can buy prepaid cell phones and/or sim cards as I travel around Europe.

But I am also interested in just what international capabilities I'd be buying, if any, if I buy an iphone5 here in the US instead.

When I visited my local Verizon store, the sales guy told me that the iphone5 is a true international phone. Using the list of stuff I've given above as the list of stuff I want to be able to do, my question is: is he right, :p or is he blowing smoke at me!? :eek:

I am aware there are many other issues at work here in deciding what to upgrade to, what plans to sign up for, etc. Right now, what I want to know is: if I buy an iphone5, am I buying a cell phone I can use the way I want to once I'm in Europe and could my wife use her basic cell phone from the US to call and text me while I'm there?