"The Inquisition" is a misnomer, there were several Inquisitions. Some used force, and some didn't. The term inquisitio simply means a particular kind of (Roman) investigative legal procedure. The concept and the name came into English common law as the "inquest".
ArrogantBustard is not being dense at all. He's trying to get people who habitually complain about Rome's "tyranny" out of one side of their mouth, and her "laxity" out of the other, to see the contradictory nature of their position(s).
I take your etymology lesson; I'm sure it's an important point in an actual discussion of earlier times.
This appears to be a letter from this century, from a couple dozen RC priests in one city. So let's cut through the fog. When the church can't remove a priest who works against her declared positions, she is at the least LAX.
The further question is why is she so lax? To an outsider, it looks like simple cowardice.