Opinions vary. I go 5k~6k between oil changes but I use a true synthetic oil (which BRP is not). Scotty is right about the crush/shear effect of transmission gears on oil. That is why most vehicles have a different compartment for gears so they can run an oil specifically designed to deal with the tremendous forces encountered there.
True synthetic oils deal with these stesses much better and for much longer than oils that are marketed as 'Synthetic' and are not. Many brands market a 'Synthetic' oil but they use standard mineral base oils with additives. The additives and the mineral based oil tend to break down quickly, hence the short change intervals. True synthetic oils also resist contamination much better than these other products.
I am not aware of any oil failure related issues with the Spyder. I am not saying there are none but I have not heard of any. Oil delivery issues, bearing failures, yes, but due to problems not related to the oil itself.
Each rider must decide what they are comfortable with and what their priorites are. If you want the best possible lubrication and protection there is no question that a TRUE, Full Synthetic oil is the only way to go. Just because it says 'Synthetic' on the bottle does not mean you are getting a true synthetic oil.
The Castrol products that BRP puts in their bottle will do an adequate job if changed often. If adequate is good enough then there you are.
Here is an interesting chart. Amsoil has their products independently tested and there are many parameters and jobs that an oil must perform. This is just one of them but a very important one.
This chart tests the oils ability to maintain it's rated viscosity in actual operating situations (hight temperatures). Film strength is the oil's ability to keep metal parts from touching. Ideally your oil will never allow metal to metal contact. This is a difficult task in a transmission, especially when the oil is hot. If you don't have adequate film strength it really doesn't matter how well an oil does everything else because you're going to get excessive friction, wear and heat buildup in components.
Just because your oil says 10w-40 on the bottle does not necessarily mean it can maintain that rating in severe conditions. And, as the oil ages, this film strength can get much weaker. A true synthetic oil will maintain strong film strength for at least twice as long as a mineral based oil.
As you can see the Castrol product does not do well here. It really is an unfair comparison though, because it's apples and oranges (true synthetic oil vs a synthetic in label only oil). But since these manufacturers market their products as 'Synthetic', charts like this are needed to show the customer what they are getting.
10W-40 Motorcycle Oil High Temperature Viscosity Protection Higher values reflect better film strength ASTM Test Method D-4683