The big discount sellers are often not authorized dealers
That is not always true. Some manufacturers do sell to (or at least tolerate) web discounters, either directly or indirectly, as a way to deal with old, B-stock or overstock goods.
and the manufacturer will not honor the warranty if you don't have a receipt from an authorized dealer
Ah, that's a whole different kettle of fish. The so-called "Grey Market" has changed completely since I was selling camera and audio gear in my college days (early 80s). This is a topic for a separate, long discussion, but I will say that for every manufacturer who decries the unauthorized market, there is another manufacturer who uses it to their own advantage. Multi-channel marketing is a reality of life - different buyers paying different prices for the same product. The retailers do it too; google the term "dynamic pricing".
But with regard to the warranty situation, this was pretty much settled years ago (in most states and in federal court) during the spate of Grey market lawsuits in the 1980s.
In general, if the *manufacturer* is responsible for the repair of an object and the customer can prove that they purchased the item new, the manufacturer is responsible for the repair.
If the manufacturer's distributor (can be a whole or partially owned subsidiary) is responsible for the repair, then the distributor can refuse repair for any product sold outside it's disty/retail channel. This is why many manfacturers use 3rd party distributors or set up their own.
There are several exceptions to these generalized rules, and many manufacturers post rules that are simply not true or legally valid. As a consumer, I would say that this is an assumed risk proposition: how much risk am I willing to take. If I am looking to buy a pair of $600 KEF speakers, I might be prepared to take more risk than if the item was a $6,000 tube amp.