Sixty million is only an estimate, because the perpetrators of the inquisitions were the ones in control of writing the histories. Finding the real number isn't possible.
The only place in which that might be true because the church was effectively the temporal authority was the Papal States, and only for the period from their independence circa 1300 to the time of Napoleon. But as somebody who majored in history, I sincerely doubt it.
The temporal authorities keep the records -- the government of Spain, for one, had meticulous records. Even if the "histories" of time did not mention it due to some sort of universal conspiracy in which the Evil Church managed to stop everybody from writing anything that mentioned it (pretty preposterous in itself), subsequent research in original documents would disclose it. People have relatives, property, jobs, friends, etc. They only "disappear without a trace" in horror fiction or other alarmist literature.
As an example, the Black Death in the 14th century killed a third of England's population. Despite the tremendous dislocation and social upheaval that this entailed, we know WHO died, WHERE they are buried, and what happened to their property. It's all in the Public Record Office and anybody can go look at it.
To think that any institution, whether the church or any temporal authority, could "cover up" something of that magnitude is tinfoil hat stuff. It's impossible to cover up the murder of sixty million people, estimated or otherwise.
The folks who are telling you this, whoever they are, are admitting that they have no proof whatsoever, because the "the authorities have covered it up" excuse (1) is completely unsupported in fact, i.e. it cannot be done; and (2) is the last refuge of a scoundrel.
What was the population of Europe at that time?
60 million? How many people do you think even lived in Europe during the middle ages? Your source is on crack.
You might want to differentiate between the Inquisition and the Spanish Inquisition--two entirely different "purges." But 60 million executions is beyond ludicrous. It was impossible. There weren't 60 million people in all of Spain, France, and Italy in the 15th century--much less "infidels."