Believe it or not there are actually folks who specialize in figuring this stuff out. According to FWP their sampling methods are more accurate than the mandatory reporting methods that many other states use. The mandatory reporting methods still don't get 100% of the hunters reporting, there are always people who don't fill out the survey. The results tend to be slightly biased toward successful hunters reporting in to make sure that they get a chance to hunt next year while unsuccessful hunters may decide they aren't going to bother with hunting next year anyway because they had a poor hunt so why fill out the survey. I've also heard of people intentionally falsifying their report to make the unit they like to hunt in look less desirable. (i.e. they make sure to put in every year that they weren't successful and they rate the unit as a poor quality hunt, even if they actually did in fact harvest).
The random sample method theoretically avoids this by selecting at random the individuals to be surveyed each year. Just like polling for elections, they don't survey 100% of the folks who are going to vote, they just pick a sample. It tends to be pretty close.
Last year I bought a deer/elk combo and I got called asking if I hunted upland birds and how many I harvested. They didn't care about my deer or elk hunting because I wasn't part of that sample.
This year I got a call asking about my elk hunting. They didn't want to know about whether I hunted upland birds or deer because I wasn't part of that sample.
I'm a CPA and we use sampling in our auditing process and you can get some pretty good confidence levels with some pretty small samples when it really comes down to it. The trick for FWP is to get a high enough sample of folks that hunted in each hunting district. Not really sure how they do that without having to pick a much larger sample than needed because they really won't know until they call folks what unit they hunted in on the general units.
I actually think a state like Montana is spending more time and effort and $ on their harvest statistics than the mandatory reporting states do. Anymore with online surveys it is pretty much just a one time cost to develop the program and pretty minimal resources to compile the data after that. Vs. I bet Montana spends a bunch of money on dozens of employees or contractors calling thousands of hunters to gather the information that they do.
Oh well, just a ramble I guess, but my opinion is that the Montana statistics are probably pretty accurate.