Well, that someone is neither you (@josephlreyes) nor @rbennett, I am afraid. 
You’d be right if the electrical load would be somehow regulated to always use the same power regardless of the supplied voltage. Such loads exist. A simple heatbed, supplied directly from the mains, is not one if those.
Any simple electrical heating element is basically a resistor, be in in an electric heating in your house, a haidryer or a 3D printer heatbed. In case of the X1C I can even tell you its approximate value: at 230V it uses around 1kW, according to R=U²/P this results in roughly 53 Ohm. Hence, the current I=U/R is around 4.3A.
Now you connect the same heatbed to 110V in the US. The unchanged resistance of 53 Ohm results in a current I=U/R of 2.1A. This again gives you a power P=U*I of about 230W, a little less than a quarter of the power you get on 230V.
This conforms to the general rule that an increase of voltage by factor x results in an increase of power by x² with a constant resistance. If you want to try this in a more practical way: get yourself a European hairdryer and connect it to a US socket providing 110V. The result will be quite disappointing and will certainly not get your hair dry in due time. A 2,000W beast will not even produce 500W.
A bit more spectacular is the opposite case: connect a 2,000W hairdryer from the US to a European 230V outlet and you will get an incredible 8,700W. The only issue (besides some burnt hair) will be a very, very short life of that poor appliance… 
By the way, there are some hairdryers and other heating devices on the market which can be switched to either 110 or 230V. For such loads this does not require any electronics but just a simple mechanical switch. In fact, the heating element is just split into two parts: for use with 230V, those two halves are connected in series (doubling the resistance of a single one), for 110V in parallel (cutting single resistance in half). This means that with the 110V setting the resistance is reduced to a quarter of that at the 230V setting. According to P=U²/R, half the voltage and a quarter of the resistance results in the same power. Mission accomplished. Whenever you find a mechanical switch for selecting between 110 and 230V on any appliance of power supply, this is the principle behind it.
Finally, the above calculations are not entirely accurate as the maximum specified power draw of a X1C on 220V (yes, they specify it for 220 and not for the more common 230V) of 1,000W is not entirely used by the heatbed but also includes electronics, fans, stepper motors, and toolhead heating (which all are supplied by regulated low voltage and therefore use the same power regardless of grid voltage). I would estimate the maximum power of the heatbed alone to be around 850W. If you do the math once again with this value on 220V, you will get around 210W on 110V. Add the remaining 150W for the rest of the system and you get 1,000W on 220V and 360W on 110V. And now have a look into the official specs:
