The above reply comes close to nailing it, I think.

What appears at face value to be a moral question is really more of a linguistic problem.

Ignoring the sort of cost-benefit analysis that you get into with the extreme cases (e.i. "Would you commit the tiniest breach of values for an enormous payoff?") look at what happens if someone just gives a simple solid "yes". Say I claim that honesty is one of my core values, but also say "sure, for $20 I'll tell a small lie and for 200k/yr I'll lie for a living." If I could make such a claim, in what conceivable sense could honesty be my core value? If you can override a value that easily, then it wasn't a substancial part of your make-up in the first place. It was only an expedient pretense, put on either to make some part of the world like you, or to make you like yourself.

If you answer a solid "no" I think it is fair to say that you have not been tested by all circumstances and are probably also just reaffirming your own image. Put me in Auschwitz and give me the opportunity to save my hide (the barest measure of material success) by stealing some other poor schmuck's ration of gruel. Then, and only then, can I give a meaningful answer to the question. Right now, I haven't the slightest idea.