If hirer has an equally good candidate or consultant who quotes a lower rate: you're out of the running. Even if you're better, you have to be better value according to the employer's own assessment.
There are few employers who are price insensitive and you have to be in an overwhelmingly lucky or privileged position to find them.
That's why, if possible, you negotiate when you already have another offer. I negotiated a +50% annual pay raise at my last job because I was completely willing to walk away for another job.
I also got the raise because I was playing an important part in a high value project at that time. I felt a bit guilty about the possibility of leaving the project in the lurch, or negotiating when my value was at its highest. I thought it would lead to resentment from my managers if they thought I was strong-arming them.
But they agreed to the rate, and never showed resentment. Every successful business person or trader knows to sell high, but sometimes the rest of us forget.
> If hirer has an equally good candidate or consultant who quotes a lower rate: you're out of the running.
If you can easily be replaced by a new hire or a consultant, you don't deserve the higher salary.
You shouldn't and you did well. Whenever you have a position of strength and the business can afford it, you should exercise it. Simple. This is business.
If someone is willing to rescind an offer because they are upset that you tried to negotiate, it's probably not someone you want to work with anyway.