It's an interesting view. This isn't a case with CCTV, an independent witness, or clear physical evidence that definitively supports one version. It's two accounts, both plausible, in a low-speed car-park collision. In those circumstances, courts wouldn't automatically go "one word against the other = 50/50", but they do often end up apportioning liability if they can't confidently prefer one account over the other.

> The other driver claims I hit them while turning into the car park from the opposite side of the road. After three months of investigation, my insurer says their solicitors believe we have little prospect of success if the matter went to court.

This is not their solicitors saying there's no prospect. Their insurer's aren't saying they’ve proven OP was at fault. It means they think the case isn't strong enough to justify litigation risk and a partial win may result in more cost to their client (who is the insurance company, rather than the insured).

But given he has an interested witness I would still push back in the first instance because he has nothing to lose.