In my opinion training and checking should be separate, checking should be a QA process to verify that the training is doing the right thing...
Dehavillanddriver, not sure why you are standing by for incoming., your statement is spot on!
Training departments should be assessing through constant feedback, things such as, is the training relevant? does the training need to be further developed? is it adequate and in some cases is it really required?
Checking departments should be assessing the competencies set by the training department and regulators.
You are spot on also with the fact that some people are born trainers, they have a passion to impart knowledge and are masters at doing it. Some people are great at assessing but cannot impart knowledge. Some can wear both hats.
The QA department can ensure that each department is meeting its objectives and ensure adequate feedback to better the process.