Perhaps. I'm not 100% sure what that 'truth' is, and if I heard it I suspect I'd LOL. At the moment they seem to run their campaign based on an all-consuming fear of UKIP/Brexit Party and Corbyn. Anti-Corbyn sentiment may drive their voters in their favour, but UKIP/Brexit Party are basically tories on crack, so that's kind of enticing to closet racists.
I'm pretty sure you're wrong on this point. If Labour jettisoned all of its 'Leave' MPs, maybe 5% would be gone. If the tories jettisoned its 'Leave' MPs, about 33% would be gone. I can cite all of the Parliamentary votes on this point. The tories also have a far larger problem with rebellion on Brexit.
As for Labour's base (members of the Labour party who are not MPs), I'm not sure. I haven't seen figures on that point.
I assume 'base' means 'electoral base' not membership. The membership are strongly pro-remain. Not only are many of the voters pro-leave, but their distribution means they could have a disproportionate effect on Labour MPs.
I think there's also another issue - the need to avoid an irredeemable divide among the population of the country. Perhaps that ship has sailed, though.
The Tory party has been captured by Brexit-Ultras. While all the media and the centrists were banging on about the evil commies and IRA-supporters secretly taking over the Labour Party, they failed to notice that the far-right has been quietly taking over the Tories.
As far as jettisoning 'leave MPs' goes, Kate Hoey comes to mind. She's pro-Brexit, pro-gun-ownership, pro-fox-hunting, pro-Ulster-Unionist, anti-cyclist and obsessed with 'country issues', and yet, bizarrely, represents an inner-city constituency that includes Brixton.