These things tend to have air inlet, fan and heater element ducted together bit like a fan heater inside an outer box in which the drum turns, the hot air forced into the drum from the outside and exhausted through the centre at the front. Inevitably lint builds not only in the filter on the exhaust side but also some falls through the holes in the drum into the outer box.
Some how, if your theory is correct, dog hair hair is coming into close contact with the heating element to the extent that ignition is taking place, or the temperature of the air coming from the element is sufficient to ignite the residue dog hair and lint in close proximity, or there could be spontaneous ignition taking place as a result of biological, or chemical action in proximity to a heat source, and oxygen from the air flowing by. Humidity could be another factor.
Air flow in the drum will be dependent on the size of the load, the nature of the materials in the drum, the availability of a good flow of inlet and exhaust air, the amount of water in the materials in the drum. The fan performance will be optimised for a certain combination of these. There will be a positive pressure in the cabinet and some leakage around joints etc is inevitable.
Here are some thoughts.
1- I would guess dog hair due to its mass compared to a fragment of lint may be more likely to remain in the drum and pass into the cabinet than a fragment of lint. There will be a factor as to the nature of the hair itself as to whether it iis likely to pass through the filter or the percentage that will do so.
2- If the lint filter or exhaust hose are obstructed then the fan will speed up, temperature and humidity in the drum may increase depending on the stage in the cycle. As the air flow drops the heating element temperature will increase, the radiated heat in the vicinity of the element will become a much more significant factor.
3- As the fan is then outside its optimum rating could turbulence arise inside the cabinet close to the fan itself which could cause air from the drum side of the fan impellor to pass back to the inlet side taking with it any lint and hair which will be deposited on and near the heating element, rather like our fire pumps slipping water against a closed delivery?
It may be worth a FINDS message to see if this is a common occurrence.