Well you are right but you don’t need tier 4 (Student Visa) if you already have a Tier 2.
Also i want to add NHS don’t even offer the placements to all the Medical students in uk and i know quite few doc’s from MMS who were denied the placements and currently practicing in KSA.
NHS do offer the scholarships but only for British native students/doc and very few for European students. I wonder they will offer any scholarship to anyone on Tier 2 visa.