Whilst the DWP have historically contacted GPs for DLA, this is not the case for the vast majority of ESA claims, you need to decide whether your GP really does believe they will be contacted or whether it is an excuse not to help you.
A more sympathetic GP may be willing to help you but unable to provide anything of value because they have not seen you before and can only rely on your medical notes.
It's a decision that only you can make.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems