I'm not really sure where I fall in all this, to be honest. It was a complete accident when I stumbled across some boots of the Essen production Phantom on youtube, and from there I tumbled headlong into my love for German musical theater. Because of it, I've worked to become fluent in the language, and I've made several overseas trips to patronize their stages. (Tourism money, yay!) Less a case of "watch the bootleg instead of go to the theater" and more a case of "go to the theater because I fell in love via bootleg". I like to think of it as a positive cycle of reinforcement.
I would say there is a difference between recorded theater and a bootlegged movie, simply because theater is entirely location-specific. A movie, though, can be transported anywhere and is always the same. There's no reason to boot a movie other than being too cheap to pay for it. A live show, though: I could see a show live twelve times, and still wish I had a recorded video of it, for when the cast changes / after the show closes / when the tour moves on, etc.
That being said, I love when shows release professionally filmed DVDs, and keep those right along with my cast recordings, for much revisiting, and for sharing with family/friends (particularly in the case of foreign musicals. The ability to add my own subtitles and render it understandable to English speakers is a big plus). I treat it much the same as how the 04 Phantom film, for all its flaws, led to a group of my friends heading to BWay to "see it for real". Similarly, I am excited beyond words for Rebecca... because I've been watching pieces of the Vienna production on Youtube for years, wishing/hoping/praying it would come.
Without the existence of boots, I'd be far, far less interested in theater than I am today... and would have spent far, far less money on it!
None of which has anything to do with actors watching their boots.

Though I'll say it goes both ways... I've had actors recommend various boots of different productions at SDs, in interviews, in casual conversation, and so forth. Not in a "let me show off" way, but in a "you might like this if you get the chance to see it" way.