I'm sure the video shop owners are grateful for your cash. In reality they're the only ones getting it. The DVD has been purchased, the producers already got their cut of the disc you're renting.
Then there's the question of libraries and timing. If a DVD is available from my library is it any less ethical to download it than to borrow it? How so? Also worth pointing out that when this documentary was released there was a period of a couple months where you could watch the doco in full for free on the documentary producer's website. How would taking a screencap of the film from there and watching it later differ from taking a copy from thepiratebay?
I applaud your commitment to paying creators for their work, but I'd recommend reconsidering where and how you make that happen. Renting this from the DVD store doesn't help anyone but the DVD store owner. No change in exposure for the topic, no change in view count or ranking of the DVD and certainly no change in financial or social situation for the Shulgins. You're better off buying a copy of TiHKAL and PiHKAL if you want to send your cash to these great humans and to spread awareness of this exceptional man.
I do not applaud your self-righteous anti-piracy screed since me pointing people to where they can get the doco for free unarguably increases popular awareness of the Shulgins far more than telling people to rent the DVD.