If anything the rules have changed considerably since we arrived 3 years ago before all this CSI stuff and proof etc.
The CSI was a requirement if you only arrived 3 years ago. That CSI requirement for free movement was brought in by the EU 13 years ago in 2004, under Directive 2004/38/ECI.
The rules on proof hasn't changed as it has always been on the EEA citizen to ensure that they are lawfully residing in another member state
at all times after that first 3 months the EU allows them. That is why the end date on an RC means nothing as an RC becomes invalid if the EEA citizen sponsor ceased to be a qualified person.
The UK has just got better at checking for all this when they apply for British citizenship by having an EU application checking team at UKVI. This EU team was started long before the Brexit vote in June 2016. And the 2015 Immigration Act made working in the UK when not being in the UK lawfully, a criminal offence from June 2016.