It bothers me when parents feel the need to do that.
I mean what are they trying to accomplish anyways?
Does she want Susie to straight up say
"Yep it was me" 
I'd also be a bit taken back by DCM feeling it's appropriate for her to reach out and touch another child.
Imagine if you said
"Yeah, Susie's dad was here earlier and when he felt Mary's head he said she was really warm" I bet she'd be upset about that.
As for blaming illness on others I would turn it back around onto her and start really buying into how much others spread illness to her child and since mom is right in wanting to protect her DD, you're going to have to start calling her for pick up or telling her to stay home ANY TIME any of the other kids have a sniffle or a cough or any other symptom that could lead to a cold or other common winter illness.
Make sure to let her know that you are glad she brought this concern to your attention so you will make a point of being extra diligent about it from now on.
Mom wants to play that way, then play that way.
Just be better at it than she is.
