Why do relegated league clubs believe this? It can only be self-delusion born out of desperate hope that they'll be different.
Since the end of the 2004-2005 season these teams have been relegated to the conference : Kidderminster Harriers, Cambridge United, Oxford United, Rushden & Diamonds, Boston United, Torquay United, Mansfield Town,Wrexham . They're all still with us and realistically only one has any chance of going back up this year.
In the same period these teams have gone up : Barnet, Carlisle United, Accrington Stanley, Hereford United, Dagenham & Redbridge, Morecambe, Aldershot Town, Exeter City. None of these teams came straight back down and none will this season.
Why would anyone believe there is a gap in class between the bottom of League Two and the top of the Conference? If there is one it's a gap which seems to favour the conference teams.