I'd say that if the board in HE is 'royal friendly' that increases the chance that all 7 will get a royal. And if the board is 'royal unfriendly' it decreases the chance of all players. I'd think (without doing the math) that that exactly outweighs each other, so you can do the math for 7 independent hands and it gives the same results.

But that's just an assumption I have no facts or math to base on.