Sounds like they are really good tenants - because they called you and it wasn't something you all "discovered" at move out. Moisture in our environment is a real issue and although I haven't heard of this situation, your uncle's explanation makes sense to me.
Depending on how bad the damage is, I would get a quote from a reputable carpet cleaning company and if it's a reasonable amount and they expect it to come clean, offer to split it with the tenant. If the carpet cleaning pro is hesitant about whether or not it will come clean, get another opinion. If it's a consensus that it's not likely to come clean, move on to getting flooring replacement estimates. This all needs to be done ASAP - no time to waste with a moisture problem.
I would first ask the tenant how they plan to take care of it, if it ends up needing replacement. If they sound like they are unwilling or unable to pay for it, I would then offer to share the expense to take care of a good customer. Carpet for one room, if you go back with that, is a pretty low cost flooring. This is not something that can wait until they move out. If you know it will need replacement when they move out, you effectively have reduced your security deposit by what it will cost to replace the flooring.