The swab isn't for typing, it's to prove you have it.
Studies have shown over and over that up to 40% of patients with "influenza like illness" are actually infected with other viruses, principally parainfluenza, RSV, and strains of coronavirus.
Tamiflu has no activity against any of those viruses, so prescribing Tamiflu because someone has "all the symptoms" brings those people side effects and costs with no possible benefit.
Tamiflu doesnt have any appreciable side effects and if the flu is going through an area, theres no reason to lay to type obvious symptoms.