I think there's a few factors at play here.
It depends on whether she made up the conditions totally or exaggerated minor complaints.
I know I've walked out of a doctors feeling relieved that dc hasn't got to take it further, and other times relieved I've been taken seriously and it is being taken further. My GP tends to believe mums as he says as a standard rule if the mum says she thinks there's something wrong it is worth investigating.
2 of my dc this year have been investigated (nothing more major than blood tests though) for things that have no proof-or certainly I could have got the dc to fake, and are mostly on my say. In one case it has gone down on DLA application (although as a side issue, the main issue isn't fakable!)
I am very thankful that the GP took me seriously for both situations because although neither has turned out as bad as it might be, if it had been worst case then time was very much of the essence. Ds was fasttracked in for a paed appointment-nothing except what I said, some of which was along the lines of "he just isn't right and I'm not happy."
However I do know of parents who have tried to fake and get their dc involved in faking for school applications. I knew the SENCO at a local junior school where the nearest secondary was failing and they all wanted to go to the further one with a catchment of about 50yards.
She said they would have 2-5 (out of 60) children, always pfb, who usually around summer term in year 5 parents would come to her apparently concerned and wanting them statemented. Having talked to the teachers they would say there was no issue. When this was fed back to the parents it was not uncommon for the child to apparently suddenly produce behavioural issues.
They usually went for autism spectrum simply because it is hard to diagnose etc. although they had one child who got fairly far along on visual impairment before it was found to be faked. They have had conversations with the child where the child says something along the lines of "My mum says that if I don't behave like this/tell Dr this then I will have to go to the rubbish school."
She used to solve the issues usually by telling the parents that she has happy to investigate, however they had to realise that it was a long process and the statement wouldn't be through before applications had to be in for secondary. Most issues disappeared overnight from that.
The problem with ASD is that it is variable on where the child is so they have to listen to the mum. It also varied by child. It's not uncommon for a child to be able to hold it together when out, but really kick off at home. If Drs don't believe that is happening, then far more children who need the support won't get it than parents will fake it.
Should we tell doctors to ignore parental concerns on the back of this one case? Not at all. Far more children would be hurt by lack of investigation.
Should lessons be learnt. Yes, but that still doesn't mean avoiding investigating potential serious issues that only mum has seen.