If they're so legit, they should be happy to share the footage.

Put the moral implications aside for a second and translate their actions to any other business. The business being ok with sharing the footage obtained via trespass implies that they're also ok with trespass.

That's a legal minefield no business wants to get into and out has knock-on effects. If employees are identifiable and haven't given consent - and they are not in a public place , working in a private area - then that's another headache.

If they use proprietary methods or equipment it gives a chance for competitors to gain insight and possibly an advantage if they happen to view those methods.

There are health and safety requirements as well. Regardless of who is on their site, they have a duty of care to protect them from hazards. Having people on site that aren't aware of safety processes (and processes in general) isn't great. If the trespassers method of entry was relatively easy, it means that protections that stop the general clueless public aren't the best either, and that puts them in hot water with safety regulators.

So basically, no legal counsel will tell the business, "sure, let them show the footage they illegally obtained, it'll be fine". They have to resist it, regardless of whether it's a shining example of best practice or not.