First off, I'm not a germophobe.  I don't carry hand sanitizer and I don't lysol wipe everything under the sun.  I've got a great immune system and hardly ever get a cold.  My DD was 5 months old when she was at a sitter with 10 other children.  Kids get sick, and I agree about wiping out our immune systems by using too many disinfectants.  However, putting my child at risk because I feel the need to help someone else, not going to happen.  Maybe OP should have climbed under the door instead of having her kid do it.  I'm sorry, but I don't think most adults would do it, and I don't think it's fair to ask your kid to either.  Not just what they touch, but probably get "stuff" all over their clothes and then spend the day like that?  
As far as helping strangers, I have been trained as a fire warden in my high rise NYC office building for many, many years and have also been trained in the use of an AED and CPR.  During our last recertification training for CPR our instructor posed a question -- you come across someone who needs CPR breathing and you don't have your face shield.  What do you do?  I said, well I'd perform CPR breathing anyway.  WRONG!  He said under no uncertain terms should we even consider it.  Do whatever you can to help WITHOUT putting yourself in danger.  He suggested doing the chest compressions without the breathing because "something is better than nothing."  But as he said, in this case, the person may be beyond help anyway -- why put yourself at greater risk if the conclusion might still be the same anyway?  He also pointed out that no EMT would ever do breathing without a mask, so why should I feel compelled?  My point being, these are decisions we made as adults, and deal with the consequences as adults.  I don't feel you should ask your kids to do something you might regret later and crawling through urine and feces is definitely something you might regret later.  Or to put it another way, wouldn't you scold your child if you turned around and found them crawling around on a public restroom floor?  So it's okay if you ask them to, but not if they decide to do it on their own.