Yes, being dishonest during a negotiation often torpedos the whole interaction.
I tend to think there is a pretty broad space where most reasonable people will agree to what an honest discussion looks like.
Just remember, when it comes to companies and compensation, there are myriad ways a company can not lie and still mislead you.
I have been in this situation in the past and it's always the right move to walk if they won't come to the table when you ask politely.