If you have inflation, you do not have a gold standard. If you have the gold standard, you do not have inflation. These are definitions, not arguments.
This is demonstrably false. Just look at a graph of dollar value from 1790-1913 and try to reconcile what you just said with the extreme spikes between inflation and deflation that occurred on extremely short intervals.
The truth is that for the last few centuries credit has made up the majority of the money supply, not currency. Even on the gold standard banks could inflate and deflate the money supply at will by manipulating credit and in fact that's where all the depressions in the 19th century came from - all the banks would agree to stop making loans on a certain date and crash the economy so that they could foreclose on everything.