UA is likely to argue that a delay caused by airport congestion is out of their control. In general, compensation is not provided for things that the airline can't control. You would have been on more solid ground if the delay were caused by maintenance or crew scheduling.

Minimum Connection Time is a standard air travel concept. Airports and airlines work in conjunction to publish them. Airline reservation systems are set up to enforce the rules -- the search engine won't list connections that don't comply with the MCT, for example -- and travel agents will not sell a ticket that violates it. So, yes, it's absolutely something that UA will understand.

The best time to use MCT information is after a schedule change. If she had called when she got the schedule change notification, and said "due to the schedule change, my connection now violates MCT," UA absolutely would have re-ticketed your friend on any reasonable itinerary. "Reasonable" is fuzzy, but, in general, any of these choices would have worked, in approximate order of priority: an earlier UA flight into PVG, a later HO flight to BKK, a later flight to BKK on another airline within Star Alliance, a later flight to BKK on a non-Star Alliance airline*, or changing the connection city to another location where UA flies.

UA should have re-accomodated her in advance anyway, but a search of the schedule change thread will tell you that they often drop the ball on this. Unfortunately, this is where your friend's inexperience came into play. Someone with experience transiting China would likely have seen a sub-2 hour transit as exceptionally risky and called to ask UA to fix it. (Even if the connection were technically legal, UA tends to be very flexible in these situations, so there probably wasn't even a need to look up the MCT -- or even to know what "MCT" means -- before calling). Rest assured, she'll keep an eye on schedule changes like a hawk from this point forward.

So, long story short: Your best argument to UA is something like this: "Your system rebooked me onto flights that violate the Minimum Connection Time -- specifically, the three-hour minimum for international/international transfers at PVG to Juneyao. This mistake was compounded by an arrival delay of my UA flight into PVG, causing me to miss my connection. After UA's PVG employees originally refused to help me, I eventually arrived at my destination 20 hours late."

I wouldn't get my hopes up, but you're welcome to try. :-) Let us know what they say.

* provided that UA has a ticketing agreement in place with them. The major full-service airlines all tend to have these agreements, but smaller, low-cost airlines don't. For PVG-BKK nonstop service, the only airline I see that would have been a problem is Spring Airlines, a low-cost Chinese carrier. UA doesn't have an agreement in place with them, so they could not have routed her onto a Spring Airlines flight even if seats were available.