The PT is correct. Running/ Jogging is an advanced activity and if you are considerably overweight to obese or above jogging or running can put undue stress on your knees and feet and cause injury - if not now perhaps in a few weeks/ months and then you won't be able to do the activity until these injuries are gone. Muscularskeletal injuries can take weeks to months or even years to repair.
I got shin splints and plantar Fasciitis from just walking and it took 2 years of wearing custom orthotics before I could enjoy walking again. The shin splints took even longer. I am just now beginning to jog a bit with my dog but I am only 10 lbs overweight according to BMI charts.
You don't say how overweight you are but if the PT feels you are too heavy to begin this activity I would take heed.
If you want to begin building cardio vascular endurance start small and build up - start with waking, elliptical or even recumbant bike or swimming. These don't put the stress on the lower body like running does. As your weight decreases and you get healthy then look into a couch 2 5K program and gradually ease into running.