The HSA administrator is required to send you a 1099-SA if you had any distributions from your HSA. If there were no distributions from your HSA, then no 1099-SA is sent to you and you skip it in TurboTax.

It is certainly possible to have more than one HSA, whether because the administrators changed as in your case or because you had a previous job with a different HSA or whatever. 

It is puzzling that the one HSA sent you a 1099-SA with that note on it. Well, if they did not file it with the IRS, then you don't need to add it to your return (it would just puzzle the IRS anyway).

Use the 1099-SA that doesn't have a note saying "Account owner took no distribution for the tax year."