The reason cloth was probably in order for later "presentation" purposes for viewing my the family (or in the case of an open casket funeral). In my former line of work as a police officer we were encouraged by the local funeral homes to roll up a towel and place in under the chin until they could arrive to transport the person to their facility. The body gets harder to manipulate by the hour. Sorry if this was more than you wanted to know!
Not at all, it's interesting to hear the reasoning behind it. I figured it was something like that. We didn't have a viewing or open casket funeral (I don't think those are common here), but I suppose it makes sense to not have the body laying there with an open mouth either way, especially since it was several hours before the funeral director transported her away.

