Ha, can't believe I am talking this much shit about the RF - BUT - William is the heir, and the older brother. That is literally the bedrock of the institiution, so he has an authority that Harry does not have. So, in the scaffolding of the RF, it is entirely appropriate that he takes the 'upper hand' in terms of statements etc.
I'm not saying Harry's behaviour is rational or justified, but many on here must surely recognise that people have different experiences - or mis-remembered relationships—with different family members according to age, sex, birth order, parents stage of life at the time of your birth, etc. (Diana famously said of Harry, he was naughty like her, whereas William she saw as her counsellor. You don't have to have read much Bowlby or child psychology to recognise this might play a part in their differing grief journeys, or their emotional resilience and development. Who knows).
What Harry and William do have is the shared experience of losing their mother unexpectedly and tragically. Therefore, it is not beyond the wit of many to imagine that Harry might want William to grieve (or hold a grudge?!) in the same way that he does. eg - more wailing and gnashing of teeth maybe? But I don't think it's a competition for who is the most bereaved tbh.