Speaking to various freelancers, I think it’s hard for outlets to demand exclusivity if they can’t guarantee someone full-time work (ie 4 shifts a week), especially at the moment. You’ll see various reporters also working across ITN/BBC/Sky in a way that never used to happen.
It's obvious she's got time off, but it's not impossible to say there could be some validity to this rumour.
That tweet was over a month ago, but she never tweets over the summer (or her other periods of extended leave) so isn't an indicator of anything.
On the small chance that there is any truth in it and the same conversations aren't being had with Lewis Goodall the BBC are yet again showing that they care more about appeasing the left wing twitter trolls than they do about actually being impartial (on the basis that Laura K sticks to the facts, barring the very occasional slip up that is equally likely to negatively impact any of the major parties, while Lewis Goodall is unable to hide his pro Labour bias).