Ah, I think I see where you are confused -- your arguments seem to make more sense when dealing with a single, local database. The idea here is that you want to achieve atomicity, but you need to do it across multiple distributed databases and you want to have a system who's components have exactly the same time in order to ensure consistence across each database.

Attempting to extend the landlord example... let's say that I'm your landlord and you have to pay me £1000 each month. You send the bank a message telling the to pay me the money. The bank may make several copies of that message and keep it around for their own reasons. Now, let's say that there are employees at that bank whose job it is to do go through all copies of all messages and make sure what they say is done. If they find a message from several months ago saying "transfer £1000 from you to me this month" and are somehow oblivious to which month it is, they may transfer an additional one thousand pounds even if it's already happened. It's not an exact analogy, but...