Wouldn't it spill out/seep through?

No, it's a very common method of serving fast food pies across the country.

Looked to me as if there was a liquid proof bottom in the box.

That's exactly how Square Pie serve it. In their case I think the inner box is lined with a transparent film of some kind, cos the bottom is kind of shiny.

Ever had coffee or soup in a cardboard box?

This is the Square Pie Box

http://www.flickr.com/photos/daveknapik/402744724/

http://www.flickr.com/photos/daveknapik/402742030

Wax coated.

MaccyD milkshakes manage ok in cardboard cups

I was very impressed with the cardboard box, you don't see them in the US, nor do you see meat pies.

I was impressed that the gravy was free. It's about 50p ususally .

There are meat pies in the USA!? They are called pot pies, usually chicken or beef - you can order them in restaurants or buy in the supermarket frozen section, or even make yourself via Betty Crocker!