Actually, there are 2 tests that need to be ordered, the sputum test and the followup culture. The first can be performed in most labs, but the second is performed in labs specially set up to incubate the culture in specific medium for 4 - 8 weeks, then to take the next step and see which antibiotics the mycobacteria is susceptible to.
Some PCP's may be familiar with this, especially those who have a wide-ranging practice - such as in rural areas where they see "everyone for everything". But, professionals who see a limited class of patients, and refer complex cases to specialists, may not be as familiar.