The sell pressure comes from the payouts. If you pay out HIVE and people want to cash out their rewards, it's sell pressure. If you pay out HBD and people want to cash out their rewards, it's sell pressure for HBD, which then the stabilizer or someone else has to buy and convert to HIVE, ultimately becoming sell pressure for HIVE. So either way it is sell pressure for HIVE. When you pay people out in something they don't want, there will be sell pressure.

Where HBD can help is the stable value removes the urgency to sell it. You might still want to cash out, but it becomes less important to do so right away to not being taking a lot of risk. So perhaps you let it accumulate in your account for a while, or perhaps you stash it even longer term in savings to earn interest. The stable value is key here because otherwise it is just another speculative token people want out of if they aren't in the mood to gamble. So as HBD has become more stable we should see people more ambivalent about rushing to sell it.

Also, people using HBD for transactions gives them a reason to hold it without cashing out, since they can spend it to someone else who can spend it to someone else, and so on (though ultimately someone along the chain of spending may want to cash it out, the longer that chain, the less intense the selling pressure).