The MH-47E was indeed tested by a competent organisation. However, since the MH-47E is used differently and flown slightly different than the RAF Chinooks, there were issues found during the UK T&E that had potentially serious flight safety implications.
The context of testing is very, very important. As long as the original equipment is used in exactly the same way as the original T&E activity, then great. That is the way that the C-17, Tutor and Squirrels were procured, for example. The JSF has a multi-national team involved in the testing to ensure that the context is correct for all of the relevant nations. Once it enters service, the aircraft will depart from the original due to the different concept of operations and so on, and the aircraft will start to diverge. T&E will then be required to ensure a safe and effective system. This model, at least, will need to stay within the UK. It should be noted that most other large nations have a T&E organisation, so it is not a case of "Brits not trusting Johny Foreigner" as GrahamO put it.