I'm at work behind a difficult web filter, so I can't see the image you posted.
What software is producing the gerbers? If you're using EAGLE, it should be masking off silk wherever there is cream at least, or exposed copper. (The silk will appear on the design screens, but inspection of the gerbers will show they mask out.) Even if you're not using SparkFun's BatchPCB fab service, you might want to run their free EAGLE .drc rule check file... it will find a lot of tight or thin spots the default rules don't.
If you're not using EAGLE, and your software isn't doing that for you, then you should manually manage the silkscreen so it's not obscuring the exposed copper pads.
Now, it's quite probable that the silk won't stick well to the solder (if silk is applied after reflow), or it will be melted off the copper by the solder (if silk is applied before reflow). But I agree, I wouldn't want to take that chance.