I'm a Specialized retailer and handle their warranty processes in conjunction with our store warranty processes and policies. It's unfortunate that you had this experience, but I will guarantee you this: The bulk of your warranty process headache is a result of the dealer, partly due to how Specialized handle's it for the dealer.
1. It does make sense that the dealer needed to have the headset in-hand while still assembled on bike. Would've made sense to call the dealer first before making the trek 50 miles to them with only the headset with you.
2. False, they do not have to disassemble the bike for a headset issue. The dealer is wanting more labor dollars. Specialized customer care (warranty department) isn't at liberty to discuss with you how your independent retailer is going to handle this part of the warranty process.
3. This should've been the first time they inspected the headset that they sold you. Unfortunately, it was the second time. Regardless, that is a quick on-the-spot inspection and the dealer should've been able to quickly determine that this was indeed a manufacturer defect. Their process may involve having Specialized confirm that they will warranty the headset.
4. They don't have to contact Specialized on this. It is such a minimal warranty claim, that if the dealer was worth their weight at a reputable Specialized dealer, they will get the headset "cost" covered by Specialized without question. It may be part of their in-store policy though, and it being handled by an employee without the authorization to make that call when it will involve store costs and pending store credits from Specialized to the dealer.
5. It's unfortunate that they didn't have the headset in stock. If they were to press the issue of urgency with Specialized, they could've had the headset sent out with express delivery and have it within 1 or 2 days at zero cost to you.
6. The shop installing the headset is part of the Specialized warranty policy. This is the only way to have some sort of control as to what is truly going on with any type of claim. I could give you a laundry list of examples, but this should go without saying. If the brand you're buying from, and the dealer themselves aren't the ones doing the work on the products they sell you, there is too much gray area as to what has truly happened. This particular issue is a pretty easy one for you to handle yourself regardless of your experience. But, say you installed the replacement headset improperly, or the headset was loose... and it wallowed out the bearing compartments within the next 30 days of riding, and this process has to continue.... That is the nature of what would likely happen to most consumers with most of their issues. Doesn't mean that you personally would've done that, but it would likely happen to most consumers for most situations.
7. This is where the shop and possibly their policies are screwing you over. And they're not screwing you over by having a policy to charge labor directly to you for their time. However, they are screwing you for charging you labor for a service that they should guarantee with a minimum of 30 days after your purchase. It should be something more like 60 days, that if something is a manufacturer defect, the dealer should cover these labor costs. They can chalk this up to a cost-of-doing-business expense, or have Specialized comp them in some way for the labor and effort on something like a headset (literally a five minute job) on a new S-Works. Also, this labor should not be done, and parts installed, without already knowing that Specialized is going to cover the cost of the replacement (warranty) parts.
8. Living 50 miles away from the dealer isn't ideal for this situation, or for most, but this could've been handled better my a more competent dealer, more competent employees, and the dealer having a better understanding of how this type of process works with their business "partner" of Specialized. Their dealer policies should either be better fine tuned, or the their staff could use some better training and that could mean from the top down.

It is very unfortunate as a dealer and as a brand to lose business over something so trivial, and it starts with Specialized and ends with the dealer giving you a terrible impression.

The only thing that you could've done differently, at least from the way you described it, is give the shop that's 50 miles away a phone call before going in. Not to say that the dealer would've handled this properly, but it should've been the starting point. At the very least, give Specialized the call first, and they can begin coordinating with the dealer before you make the trip over.

Hope this helps, and hopefully your lack of faith in Specialized's products isn't completely diminished. I would have a talk with the shop owner and let them know how this was handled and the impression it's given you of the the bike brand, and of their store's brand. They will take that seriously, and hopefully implement procedures and training to make sure this doesn't happen to their customer base in the future.