Where do you get this info? It's always been my belief that refusal means automatic conviction.
No, most place refusing the breathalyzer is automatic suspension of you license, then they get a warrant and get your blood. There’s no automatic conviction for constitutional reasons. In every jurisdictions I’ve gone through the license process in they say you can refuse the sobriety test but not the breathalyzer.
First, as your driving license is issued by your state, not by the Feds, it's the laws and regulations of your state that matter. These vary by state, as you would expect.
In PA, for example, you may decline FTS and breathalyzer if you have not been arrested yet with no penalty. From the first link via searching for "pennsylvania field sobriety test refusal":
Police officers will try to make it clear that you are required to consent by law; however, this is not entirely accurate. (What a surprise that a police officer would lie to you at a traffic stop, huh.)
According to Pennsylvania implied consent laws, you are required by law to consent to a chemical blood alcohol test if a police officer arrests you for a DUI. Field sobriety tests are not chemical tests. The only tests required by law are breath, blood or urine tests. You cannot be prosecuted for refusing a field sobriety test by an officer.
If you refuse a field sobriety test, this cannot be used by the officer as probable cause for an arrest.
Police cannot suspend your license, nor can they force you to take the test.
https://www.pittsburghcriminalattorney.com/can-i-refuse-field-sobriety-test-in-pennsylvania/
The results for the same search in California, to use another example, are similar -- you can refuse a friendly or not-so-friendly request to do FSTs.