I think the whole "but you have x privilege so you can't have an opinion" needs to be challenged. After all, who defines what counts as privileged?
It's not that a white person can't have an opinion, it's that when that opinion is 'I think this country's just lovely and definitely not racist', it should be read in the context of the experience of person voicing it. A white person is obviously not in a position to know how racist people are, given that none of that racial abuse is ever going to be directed at them.
He then made it worse by suggesting that he was suffering racism by having his white privilege pointed out to him. In addition to highlighting his tone deafness, this trivialises the racism that BAME people suffer every day in this country and suggests that it's about winning a debate as opposed to recognising and combatting oppression where we see it.
If the people at the top of the hierarchy are just going to stomp on the heads of the rest of us, there will never be equality.