Do the statements "circuits/components will only draw the current they need", and "V = IR" contradict?
It is incorrect to say "components only draw what they need to from the circuit." That statement appears to relate to questions like: "I have a power supply that is rated 2 amps and I wast to connect it to a device that only needs 1 amp. Will the power supply give my device too much current?" The answer should be something like: "The power supply determines only the voltage supplied and the current available. The characteristics of the connected device determine how much current it will draw from the power supply." Often, the characteristics of the connected device are well described by ohms law. However there are many devices that have characteristics that are not well described by ohms law. Never-the-less, it is still the characteristics of the device that determine the current in most cases. If the supply has a major influence on the current drawn, there is likely a problem with the connected device or the power supply is the wrong voltage.

Of course, there is such a thing as a current-source power supply. In that case, the power supply delivers whatever voltage is required to force a set current through the load.