It's true; only God performs miracles. The pope gets credit for the intercession, without which, the woman might not have been healed. Look at it this way. If you want a raise, you could go straight to the corporate CEO or you could approach your boss. It is through the boss's 'intervention' (request on your behalf) that the raise is given. Does that make it clearer?
Still, the CEO is the one who actually gave the raise. Me? I would go to the CEO directly.