Nobody's checking. The focus is on what you're going to spend next year's money on, not how you spent last year's money. And if you're savvy, you can use tools that were already bought for some other purpose, or that don't cost much.
Working a day job in industry isn't categorically different, except that someone is probably watching your spending more closely. You have to figure out a way to set aside some time to work on your own interest, whether you do it at work or at home.
As for money, you can get technology made for 1/10 of what it costs your employer, by choosing your battles, cutting out all of the overhead, and using free stuff.
So I moved into industry out of post doc and I can tell you as long as you're getting your day job done and it isn't that expensive you can test most any idea. I'd say it's even easier to do it in industry because "not that expensive" to industry is like 10-fold more than in academia.
Working a day job in industry isn't categorically different, except that someone is probably watching your spending more closely. You have to figure out a way to set aside some time to work on your own interest, whether you do it at work or at home.
As for money, you can get technology made for 1/10 of what it costs your employer, by choosing your battles, cutting out all of the overhead, and using free stuff.