To be clear, I don't think you should refuse a breathalyzer if you are told to take it. What I said, and what ALPA says, is do not offer to take one to 'prove your innocence'. There is a big difference.
Pulled over on the side of the road by the police, absolutely refuse the invitation to a field sobriety test. They are not mandatory in any state that I know of and it is a no-win scenario. I'd be interested to know the stat (probably doesn't exist) on the percentage of people that pass a field sobriety test. Probably low single digits or a percentage that starts with 0. The test is 100% subjective and the person grading the test is already convinced you're drunk or he wouldn't ask. A sober Olympic gymnast could fail it.
If a cop tells you to take a breathalyzer, there are many states where refusing to do that also is an automatic suspension of your driver's license, which is probably where the FAA got that idea.