'special attack' is a separate type/category/multiplier. 'character' is one multiplier, 'element' is another multiplier, 'special attack' is yet another multiplier. So, it can be rather potent, depending on the restrictions. It's like how the vigorous skill (which also counts as special attack) has some nasty potential, but realizing it is a bit strict (you need at least near full HP).
For the event eidolons with that passive (at MLB), it gives [10 + 40 * (1 - HP/MHP)]% special attack. So a minimum of +10% at full HP, then gains +1% for every 2.5% HP lost.