Comment 4 for bug 410846

The transparency effects in Illustrator have been achieved via masks or blending modes since (iirc) Adobe Illustrator 9.
The new AI CS4 supports transparency in gradients but previous versions didn't so it is possible that the file you're using as example was created using that previous techniques. What is visible there is either a mask or a black and white gradient that should be blended with the multiply or screen modes in illustrator.
You can try moving those elements to a new layer and use the screen or multiply blending modes, according if they are highlights or shadows (in your example they look like highlights).

Unfortunately, Inkscape had some problems with the support of blending modes on individual elements, so that feature was moved as a layer effect, exclusively (at least in the UI, I guess you can ).
With this limitation I guess that it's not possible to just "fix" the importer to support that Illustrator features.
In fact, I think it would make more sense if Adobe fixes their ugly SVG exporter making those new features (gradient transprency) available in their SVG output, since SVG supports it.