Having been through this, merely contacting the potential acquirers, confidentially or not, gives the perception that the startup is or will be out of cash, anyway. Every remotely acquisitive company is getting several of these inbound missives every day and they always assume the startup is dying. I don't see much downside to a different tack at this point and, if anything, it may serve to jump-start the auction process.
As long as there are multiple acquirers, the auction may approximately-fairly-value the company.
They make the case that they have talent, domain-knowledge, and patented IP. The company may be out of cash, but it is not intrinsically out of the fight, so long as cash can be made to appear suddenly.
Furthermore, any acquirer would be able to see the company's books, removing any information-asymmetry on the free-cash point.
GP is trying to subtly let you know that you've significantly reduced negotiation leverage with any potentially interested party. There no benefit to you to publicly state your cash position.
The buyer, yes. But now they can't even spin this as strategic or synergetic. It's obvious and public that it hasn't been a commercial success yet. Granted, that's usually overstated and I don't think it makes much of a difference to most people. But it's something.
But hey - we all got an interesting read out of it.
Weakness can be a kind of leverage. If the interested party knows that the company has weeks to live, they are forced to make a quick decision or lose out on the opportunity permanently.