I'm going to take a stab at this. What you describe sounds to me like you loaded an auto-routing route (neither a track nor a "point for every turn" route) onto a device without a map set that supports auto-routing.
When Eddie asked "What maps did you get", he did not mean what dualsportmaps.com "map". He meant the actual map--like Garmin City Streets or U.S. Topo, etc. (It's confusing that dualsportmaps.com calls a set of tracks, routes, and waypoints a "map".)
Eddie asks this because the map you have determines whether you have auto-routing or not. For example, with U.S. Topo 2008 like I have, I don't have auto-routing. That is, I can't create two points and have a route automatically created between them. If you have City Navigator or City Streets (or whatever it is called now) maps, then you get that feature.
More than that, you have to "install" the map (or at least the region where your route/track is) onto your GPS device. That is, you might have the map installed on your computer and see the route the way you expect on your computer, but if you load that route onto your device without any maps, it will be jacked up.
My second assumption based on what you describe is that the dualsportmaps.com "map" you downloaded contained a "route" instead of a "track". There are several ways to identify this. Once the GPX file is loaded in Basecamp, the bottom left panel where you see the routes, tracks, and waypoints listed will tell you whether the line is a route or a track. In dualsportmaps.com, it's kind of the same thing--the item will have either a small "tr" (trail) or "rt" (route) to the left of it in the upper left panel.
In the end, whether you want a route or a track loaded on your device (or both) depends on several factors--factors a lot of folks don't quite understand, spurring an argument or two. In any case, Basecamp lets you create a route from a track and a track from a route with one-click. Double-click a route or a track to bring up the detail window--you'll see the option near the bottom.
Tracks are straightforward--they are always just a bunch of points with a direction of travel. They do not support auto-routing or navigation assistance. That is, when viewing a track on your device, your device will not help you find the next turn or distance to destination, etc.
Routes have "smarts" built into them. With smarts, comes complexity. Complexity can breed frustration if you don't know what you are doing. Routes are just a series of points just like tracks. The difference is that your systems will actually route between the points. That is, it will see your current location on the line, find your next route point, and then use smarts to get you to that next point as efficiently as possible. The smarts come mostly from the map set you have loaded. You can put as few or as many points into a route as you want. For example, I can build a route with a point at every possible turn and bend in the road. When this route is loaded, you can be assured that regardless of the map smarts that get applied, my route will look just like what I built because there aren't any other choices it can make between my points. On the other hand, I could create a 500 mile route with only a start and end point and allow the map smarts to fill in between. It might look great on my computer, but if I put that route on my device and do not load a map with navigational smarts, the route will be a straight line on my device. Also consider that I might share the route with a buddy, but if he has a different map system loaded, the auto-routed route he ends up with may not match exactly what my maps create.
That's a lot I know...I HOPE I made it clear enough.