Is this a true corollary about Ideal Operational Amplifiers?
The voltage gain of an ideal opamp is infinity, so if there was any voltage difference between the inputs there would be infinite voltage at the output.


  Ok, so this was probably a mistake right? They may have forgot to say for a negative feedback configuration.


The ideal opamp only results in a valid (converging) circuit if there is negative feedback. If there isn't, the output voltage is infinite, then infinite voltage across infinite resistance results in indeterminate current, etc.