What does the capacitor supply, that the PSU can't? Could it be discharge current?
Before you accuse me of repeating dangerous tropes, please consider making sure to discuss it with the folks at VDE, because this is what it says in their (and the equivalent european) product norms and norms for electrical installations.
When touching the positive pole of a 1V 1000A PSU (I assume DC) you won't have 1000A flowing through your body. It is not the rating current of the PSU that kills you, but the actual current going through your body. And how well that current will flow through your body depends on many things, including voltage, frequency (if we are talking AC), contact resistances, skin resistance, the internal resistance of your body, how big you are, your ground connection resistance, the duration of the current flow, etc.
There is a reason we use high AC voltage for transportation of currents for long distances.