What she's trying to do is win as many seats as possible. The LDs have done their homework and know that most of the seats they could potentially win are LD/Conservative marginals, especially those with a strong Remain vote.
The LDs were stung very badly by the coalition with the Conservatives and they're almost pathologically averse to committing to going into another coalition. Realistically, however, they're never going to be the largest party.
Swinson can't give any public support for Corbyn, if she wants to woo current Conservative voters. Not only that, but she knows that a number of the current Conservative rebels wouldn't support Corbyn as an interim leader either.
The LDs have been totally upfront about their attitude to Brexit. If Corbyn hadn't dithered so much, the LDs might not have seen such a surge in support, but I know for a fact that some of the new LD members are former Labour voters.
Swinson thinks "she can throw her weight around" because she's the leader of a party (also elected by its members), which has a good chance of holding the balance of power in a new government and wants to revoke Article 50. If people don't like that, they can vote for somebody else.
It could very well be LD votes which win Labour a GE. Swinson knows that, as do those opposing Labour, which is why she has no option but to deny in public that she supports Corbyn.