What is the meaning of the Mishna about a weeping kohen?

And here we go again with might become a continuing series...

The Mishna says [Yoma 1:5]:

The Court elders [during the days before Yom Kippur] would pass [the Kohel Godol, who was being taught how to perform the Yom Kippur service] over to the elders of the priesthood, and they in turn would take him up to the upper chamber of the house of Abtinas [where incense was prepared], and adjure him, and take their leave, and go their way saying:

"My lord High Priest, we are the messengers of the Court, and you are our messenger and the messenger of the Court. We adjure you by Him who rested his Name in this house to alter nothing [about the incense sevice] of all that we have said to you." He would turn aside and weep, and they would turn aside and weep.

What is with the weeping? Is the author of the Mishna telling us that every year the Priest and the Court Agents would break down in tears? Is that plausible? Or is it saying that the men were required to weep? And how plausible is that? Given that this Mishna was written long after the Temple was destroyed, what is its author attempting to convey?

Note: I know why the oath was required, and I know that the Gemarah says that priest wept because he was suspected of being a Sadducee, and the court agents wept for suspecting an innocent man. However, I think this explanation makes my question better. We're told by the Rabbis that from time to time Sadducees were appointed High Priest (there are at least three aggadot of which I am aware that discuss this) and we're also told that there were times when the Sadducee High Priest did manage to alter the manner in which the incense service was performed; if so, there were times when the crying described (or prescribed) in the mishna would not have occurred -- unless the Sadducee priest possessed the uncanny ability to weep convincingly on command.