So here's a couple of points in support of buying your own materials.
First, I agree with Dennis around HVAC equipment (and other specialized equipment). You should purchase these through your HVAC contractor. Why? Because this is different from building materials in that the HVAC contractor is going to be an authorized dealer for that equipment and not simply a 3rd party going to a materials supplier for merchandise. Why is that distinction important? For the reasons that Dennis stated concerning warranties as well as it eliminates the risk I'm about to describe in my second point. Bottom line, if your contractor is an authorized dealer buy through them. If they are not, you might as well buy the equipment yourself, but I'd likely look for another sub at that point.
My second point is in support of the original post in that you ABSOLUTELY should buy your own materials. To illustrate my reason why this is important I'll tell a story from my early days of rehabbing.
I hired a siding contractor to do the vinyl siding on a 130 year old home I was rehabbing. I had used this contractor twice before with great success and he came recommended by my step-father who had used him for years. Like before, he did a great job and I paid him in full. Got a ML waiver and was good to go. Or so I thought. 90 days later I got a certified letter from ABC Supply. They were placing a lien on my property for an unpaid materials bill. What happened? I paid the contractor and got a ML waiver, how could his supplier come after me? Well as it turns out my sub had gotten in over his head on a large job where the client went bankrupt. He couldn't cash flow his business so he stopped paying his trade accounts and guess what, he just disappeared, Literally. Packed up, left town, whatever, he was gone. Meanwhile ABC wanted their money and we were just finishing up the house, so I needed a clear title. My attorney advised us to pay ABC and try to recover from the sub since we had a lien waiver. So that's what we did. I ended up paying the $4500 materials bill twice, and wasn't able to locate the sub to serve suit. Even if I had found him, my chance of collecting was pretty much zero since he obviously was insolvent and judgement proof.
My point? When you allow you contractors to purchase the materials for you, you are putting a lot of faith in them. While I agree your contractors are trusted members of your team, you unnecessarily expose yourself to risk when you put that much trust in them.
Regarding the point about contractors buying cheaper through Stock and supply houses rather than you going to home depot, that's a simple problem to solve. As a rehabber I have trade accounts with Stock, Sherwin Williams, HD Supply, Ferguson, ABC and many other supply houses. As you do more business with them you will get the same discounts. I have net-30 terms with all my trade accounts, so I can float the materials just like my contractors can, except I can control that they actually get paid. There's no mystery to doing business with trade suppliers, you just go there and set up your account. Just because you're not a GC doesn't mean you are relegated to paying DIY'er materials prices from HD and Lowes. If you are rehabbing houses, you are in the trade.
Bottom line is that I will never let a contractor provide building materials again with the exception of HVAC and a couple of others that are direct materials dealers. Mine was an example of a trusted contractor, not just some guy from craigslist. Bad things happen to even the best people sometimes. Why expose yourself to the risk.