You have it pretty much correct. It's relatively common for cops to carry a portable breathalyzer - but they're nearly always used to supplement the field sobriety test, not in lieu of it. Contrary to what the person you're replying to it saying, I've never heard of it going otherwise. US courts are very skeptical of portable breathalyzers, so cops do the field sobriety test to minimize the risk of their arrest being ruled illegal.

Another thing the US does differently than many countries is that every step of the law enforcement process has to be done correctly and legally in order for a case to hold. If a cop arrests someone for DUI and the arrest was later deemed to be illegal - even if that person then failed the court-admissible in-station breathalyzer test - the whole case gets thrown out. So cops have to make sure the grounds for even just the initial arrest are rock solid.

Keep in mind these threads always have a ton of confidently incorrect answers, so take many with a grain of salt. For example, many are saying that there are automatic driver's license suspension penalties for refusing a breathalyzer, or that the field sobriety test is required to gain probable cause before using the breathalyzer. These claims only apply to the in-station breathalyzer. There is no probable cause needed for a cop to ask someone to take a portable breathalyzer, nor is there any official penalty for refusing one (though it strengthens the cop's case for arresting you).