Really, one could ethically do either one of those things; it's just that depending on the situation and your perspective, well, probably one or the other is the better choice.
Now you seem to be arguing that the choice between continuing to run a company or not is not one that has an 'admirable' option. And maybe from you point of view, it doesn't really matter.
There's a stadium down the way from my house. when the football player makes a home run or whatever, well, personally, I don't see how that matters; I don't care, and I'm mildly pissed that I'm going to have to pay for the bonds to build the eyesore. But even so? I don't go to football forms and tell people that the large man getting the ball in the hole or whatever isn't an admirable achievement. It's the game those people want to play, and that's fine.
I personally find business really interesting, really in a similar way to the football fan. Most of this stuff doesn't really matter. Some of it does, but even that stuff doesn't matter as much as people say it does.
To me? the decision to give the money back to the founders, rather than shitting the money away when you know you have been beaten, is admirable because investors seem to select for overconfidence; quitting before you've spent every cent implies that you were able to project that overconfidence to the investors, but that you were able to remain a rational person.
I mean, it's not world peace, sure, but it implies some attributes which within the context of the business game are pretty important.