Very, very few of the medals worn by any Royal when wearing military uniform are 'earned'. Certainly not in the sense that Harry earned his Afghanistan medal or the DoE his WWII medals. For example, all the royals, alongside all serving British service personnel, will receive the Diamond Jubilee medal. It means nothing other than you are in service to HM on the special occasion.
But this is not just a British thing. Does anyone really believe, for example, that Albert of Monaco earned all the medals he had pinned to his enormous white wedding monstrosity in the Monaco 'Armed Forces'
(does such a thing even exist)?
The issue with William and the IG - they don't just have one uniform. There are several different types of uniform which an officer in the IG can wear - not just the red tunic.
Apparently William wanted to wear the uniform he wore to drive out of BP in the Aston Martin which he also wore here:
Kate and the Guards
According to William the Queen put her foot down and he wore the red tunic.