I can understand why the term white privilege is offensive to some people. Many white British citizens live in poverty and abject states of deprivation. Over the last 10 years many have slid into poverty, our society is less equal than it has ever been. To bandy around words like white privilege is bound to be hurtful and add insult to injury, although the phenomenon obviously exists.
The expression is just another way to polarise society. There are many people of colour /BAME who have advantages beyond some white Brtish people's dreams. These are often privileged immigrants who come from well to do backgrounds in their native countries, many of whom are very well educated and have opportunities to work in well paid professions.
When all else is equal, a person of colour / with BAME heritage is disadvantaged compared to a white person in this country / the US / Europe.
However, looking at the overall picture, using the term white privilege can be offensive and polarising.
I dislike polarising language and find it simplistic and populist.
It really grates when a few posts into the thread a poster just drops the "it's white privilege" comment.
It's reductive and offensive. I'd understand it more if they had said it's structural / systemic / institutional racism. Anyway, as it stands, the reason this wasn't on national news may be due to the particular family situation in this case.