As a Captain for Southwest Airlines Company, maybe I can clear up some of this...
Most US Airlines (Majors) don't require any TPIC. Southwest requires a minimum of 1000 TPIC. However, the successful applicants generally have many times the minima.
With respect, I fly for the biggest regional in the US. Maybe things have changed since you were applying to the Majors, but almost all now require TPIC. I personally spoken to several Major airline hiring departments at a job fair in Las Vegas earlier this year. I was informed that when they start hiring again there will be a 1000 TPIC requirement. I know that JetBlue are an exception to this rule, but otherwise it still seems to be the norm.
Curious: Is it legally possible to operate as a first officer for a US based airline without having the relevant type rating? E.g. only the captain has the rating in his license?
FOs over here at most airlines generally have an SIC type. They still go through a type rating course but the final checkride is not quite as comprehensive. However, an increasing number of airlines are now giving full types to those in the right seat as well as the left.