the part your missing, and I promise this is my last reply, is that if everyone had trail cameras and they asked how many cameras you had, how many days they were out and how many deer you saw, then they could extrapolate that to get reasonable numbers the same way they do asking how many you say and how many days you hunted. The numbers would statistically be the same, just the calculation based on different data would change.
But what you want to do is add artificially high numbers from your cameras into the old math models and again not provide apples to apples numbers and then the calculations are useless and the data is useless.
One way isn't better than the other, its just that you need to pick a way and stick with it. People who are adamant that they know better and provide oranges into the apples calculations mess it up for everyone.
In fact that most accurate method is aerial surveys, which they have done in the past, but they don't have the budget for that all the time. If they count a 1000 deer in an area from aerial surveys, and then the hunter reports tell them that 2000 deer were seen by hunters, they do the math and figure that 50% of the reported "seen" rate is the current population. Simple. But when everyone reports how many they saw on their cameras and they get 6000 seen, then their calculations show 3000 as the current population.
I hope I made that clear enough to realize that I'm not arguing that one way is better than the other, and they may change the method someday, but for now the method is the method, so just answer the question they asked.
If you want to suggest to them another method go for it, but until they change the question and thus the calculations, just answer the question. Your way overthinking it.