When direct-to-consumer happened, there was typically not any difference between when a large rental chain got a disc and when I could pick mine up on Tuesday morning at Best Buy (or get it in the mail, sometimes arriving the day before) or wherever.
Some chains like Blockbuster did sign rental agreements with studios both because of the bulk orders they needed and because for a few years, Blockbuster had to stock VHS tapes AND DVDs and the studios would basically make them sign those agreements if they still wanted to get VHS tapes -- but nothing stopped them from carrying the home release versions from retail if a rental copy was not available. And as you say, nothing stopped the indie shops from buying Tuesday morning at 10am and then immediately putting them out to rent.
If you want to get a copy before it’s for general sale then you need to sign a contract, if you buy it at Walmart you don’t.
However, the physical disk is protected by First Sale Doctrine. You can sell it, rent it, auction it, destroy it, whatever you want. The same applies to, say, your laptop. You can do whatever you physically want to your laptop, even if you can't copy your Windows license wherever you like.