I also can't think of a reason for which anticoagulants would specifically change DCS risk. Such meds typically affect proteins in the clotting cascades and AFAIK, these aren't associated with gas exchange or solubility in tissues.
OTOH, during a DCS hit or treatment, there may be a coincidental benefit to being on anticoagulants or anti-inflammatories. I'm not on top of the subject but IIRC, although not convincingly proven, anticoagulant or anti-inflammatory agents should reduce clot formations which follow micro-bubble embolic events. Then theoretically, there's a lower potential for thrombotic complications. Of course, this idea in no way recommends routine prophylactic use of any type of anticoagulant or anti-inflammatory. As already noted, there are other bleeding risks with anticoagulants and not only for cuts and scrapes.