Define "strike against you". Did they say it will impact your NCB?
If not, this is perfectly normal. Whether or not it will impact future premiums will depend on the rest of your recent driving record. All insurances will ask "Have you had an accident in the last x years, regardless of blame". It sounds like this "strike" is effectively answering that question for you.
When I queried this with my insurance after that pile up on the A5 where some bint took me hard up the arse, forcing me into a position where I subsequently got rammed hard by a bloke and his son, it turns out that statistically once you've been involved in a no fault accident, you are more likely to be involved in another.
So, in essence, if it doesn't impact your NCB, grin and bear it. It may impact future premiums, irrespective of your insurance accepting she was to blame or not. And, as I found out, you can't pursue additional premium costs against the other driver, because it is not yet known if their will be an increase.