I guess it depends on the recipe. If you are using the Wilton BC recipe (I use 1/2 shortning 1/2 butter) it doesn't...
But I just tried a recipe today that is alittle more greasier than I would have liked...I didn't realize I should use a different shortning brand. I might not even be able to find it where I live.
What recipe were you using?
This may or may not help,but....I used to use the Wilton Classic Buttercream icing, taught in my 1st wilton class...that was all Crisco. I never noticed a real greasy taste, but could definitely tell the difference in it and cream cheese, for instance. THEN I started using a 1/2 & 1/2 (crisco/butter) recipe from cc and could definetly tell a difference at that point.....when I made the classic recipe again it tasted greasy.
So, I love the 1/2 & 1/2 recipes now. They have no greasy taste!!! Much better. When I now make the classic (upon request) I really tell the big difference....now I am just rambling 
It probably depends on your taste preference and what brand shortening you are using.
I use Walmart brand, because it still has the TransFats. The crisco has changed and now doesn't work as good. I am not sure if a greasy taste is a by product.
Stepahnie
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