Yep - all recently trained doctors will not recomend an X ray, except if other symptoms make suspect pneumothorax. Patient nags then they will - bit like prescribing an antibiotic - makes the patient feel better if they've been told it's broken.You only expose yourself to radiation if it will change your treatment. The treatment for broken ribs is nothing, just take it easy and wait. Hence most doctors would not order an xray unless they had reasonable grounds to suspect something else which would change the treatment.
The general rule of thumb for broken bones is 6 weeks to heal. Ribs constantly move with breathing, coughing, laughing etc so might take a bit longer.