Problem with short circuit
Resistance is defined as the ratio of voltage across an object (the 'resistor') to current flowing through it. It doesn't matter if other components in a circuit are drawing more current, when a particular voltage occurs across a resistor, a certain current will flow through it - always. 

So long as the voltage remains constant, adding other components in parallel makes no difference to the current an individual resistor draws. Consider the 3 circuits below:- 







simulate this circuit &ndash; Schematic created using CircuitLab

In circuit A, R1 draws 5v/5&ohm; = 1 Amp. In circuit B, R2 draws 5V/1&ohm; = 5 Amps. In circuit C, V1 and V2 are replaced by a single 5V supply, and R3 and R4 are in parallel. Both resistors get 5V, so R3 draws 5V/5&ohm; = 1 Amp and R4 draws 5V/1&ohm; = 5 Amps. 

In a 'short circuit' situation the total current may be limited by other components in series, or by the power supply itself. As a result the voltage drops and the lower value resistor 'steals' some of the available current from the other one. However the current will still split between them in proportion to their resistances.