No, but adding direct access to specialist is going to make that problem worse not better. What adding more GPs does do is allow a return to the situation where it is easy to see a doctor in the first place. Most people needing appointments don't need specialists, but they may get worse if they can't see their GP and they may even end up falling back on more limited and more costly emergency treatment options if they can't see a doctor in a timely fashion
These are very rare stories, which is why you hear about them. There's no great reason to believe that a specialist would have taken a different view and it is an inevitable part of any system with finite resources that doctors aren't going to be keen on sending patients for scans they don't think they need.
How did we get to the situation where stuff that was considered entirely normal is now considered extraordinary? Same-day appointments were absolutely the norm everywhere I lived when I was still in the UK.