Numerous people have been told by their dealers that if they use a synthetic, or any non-HD brand of oil for that matter, that it will void their warranty.

Not only is this wrong, but it's illegal according to the Magnuson-Moss Act of 1975. The Amsoil site has an excellent explanation:

Magnuson-Moss Act Explained

Now, of course, Amsoil is going to claim that using their product doesn't violate the terms of your warranty, but it really goes for any oil of the proper viscosity range that meets API specifications.

A Brief Explanation About API Ratings
An interesting marketing ploy is being undertaken by certain companies trying to scare people into using only their oil.

The American Petroleum Institute, or API, sets standards and awards ratings for oil. These standards are awarded codes like SH, SJ, CE, CF, etc.

So what a manufacturer might do to try and force people into buying only their oil, is to specify an obsolete standard like SH, because you can't find SH oil anywhere anymore. To get around a violation of the Magnuson-Moss Act, they'll also allow you to use an oil suitable for diesel engines like CF.

The thing is, each API standard has to be backward compatible with all oils that came before it. If an anti-wear ingredient must be decreased for some reason, an anti-wear ingredient that is proven to work just as well or better must be substituted.

David Canitz, Technical Services Manager with Royal Purple LTD, answers the claim that SJ or later oils don't offer the same level of protection against wear as SH oils with higher concentrations of zinc/phosphorus anti-wear compounds like ZDP and ZDDP:

"You've bought the marketing line hook, line and sinker by the motorcycle manufacturer's that using a "car" oil rated SH or SJ will result in increased wear on your "unique" cam and crank setup on motorcycles. You do realize that when an oil is formulated to meet the newer SJ and now the SL, that they have to be backwards compatible with all performance testing (including wear testing) of an earlier oil spec. This means that an SJ oil, although it may contain less ZDDP than an SH or SG product, had to meet the same wear tests. The additive manufacturer's have to develop oils that resist wear in car engines just like motorcycle engines. Answer me this: why do your Harley cams present a harder lubrication problem at 60 hp and 5500 rpm when the same oil could be used to lubricante an engine with 200-300 hp and 7500 rpm? Both have flat tappet or roller cams. Both have bearings of some sort on the crank, either plain (journal) or roller bearing as in the case of HD. The oil doesn't have artificial intelligence. It's a marketing [technique employed] by the motorcycle manufacturer's that they want you to buy this "special[sic] motorcycle oil" at a very high price (and profit) margin."

If a warranty claim was denied due to the use of a more modern oil, a class action lawsuit of staggering proportions could result due to the clear violation of the Magnuson-Moss Act.