It's not a very popular opinion, but I don't think any grower really knows what strain they are growing anyways. I think the strains have been so mixed and matched, and probably some growers will call theirs a specific strain just to sell more of it. And with how long Marijuana growing was underground, the sources of the seeds are totally undocumented. It's basically like a big game of telephone at this point.
AFAIK they mostly grow from clones, and thus, would be completely unaffected by pollination. Unless I misunderstand plants, pollination impacts the seeds produced, and therefore the subsequent generation. So long as it keeps being cut and propagated, rather than grown from seed, you could be relatively certain of near identical genetics.
For example, every apple variety out there. Every potato variety out there. Every garlic variety out there. Grape varietals. All gone because their clone lines expired. Not being able to propagate clone lines is why we can't have seedless oranges or watermelon or grapes.
There is also little evidence that the strain has any effect on the pharmacological effects of cannabis, beyond the amount of THC per gram of flower (potency). Although it can greatly influence the smell/taste, which is meaningful.
However, if you’ve tried the “same” strain from multiple growers you’ve likely found that the smell can vary significantly, and (as a consumer) there’s really no way to know what the flower’s aroma (and appearance) will be without direct observation. This is aligned with your hypothesis.