I'm not sure the article actually says that. It is criticising the lack of integration between primary and secondary paediatric services, and looks to lack of understanding of the role of GP by paediatricians as well as vice versa. They mention potential over-referral, but balance that with reference to pressure from worried parents.
The difficulty in managing complex and long-term childhood conditions, especially when the patient has to visit multiple different specialists seems to be a greater concern. The article is about the state of services for children as a whole, not a specific concern about GPs (though it does rightly point out that further reduction in paediatric training for GPs - something that has been chipped away at in preceding years - should be resisted).
The Swedish model, which attracts particular praise, has a different underpinning system in terms of provision of hospitals, and also the Netherlands which has a transmural system.
The new proposed new role of GPs is described as unlikely to help solve the current lag between Uk and other European children's health provision.
The factor which they describe as likely to cause a deterioration in in care is the plurality of providers in secondary care.
That factor was also mentioned, for more than just paediatrics, in the recent BMA deliberations.