It would be “do your job best way you can do it, but expect others to screw up”.
And this advice is not only regarding code, but everything you work with. If there is some chance that something can go wrong, eventually, it will go wrong. If there is possibility of Database getting files corrupted, eventually it will. If there is possibility that some query will take too long and as the result of it, your system will become unresponsive, it will. Your hard drive can fail, compilator can generate incorrect code, data can be not written when OS says it was. On some “perfect friday” it will happen and come from nowhere.
When you are writing software you should always expect different pieces of it to fail. Thinking of possible failure while designing software will make you are better developer. Why? Firstly, because you (hopefully) will create code to deal with potential errors and check returning results of functions calls. Secondly, it will change the way you design your code, so failures in external system have smaller bounders and are easier to recover from. Also, it will clarify your view of interaction points and come up to idea of having general error handling policy, which is always a good thing to have.
As an evolution of this view, you will later realise that you should include yourself in the list of others who can screw up. Yes, all of us makes mistakes :) Accepting that you can make mistake when you are writing new code, or adding new functionality to old code can lead you to unit/integration technics again. These things exists for the only reason that developers are making mistakes.
And you should not forget the first part of the advice. Regardless of expecting others to screw up, you should do your best to do you job well. Thats how you can become good developer, appreciated by others.
By the way, this approach is really useful in life too. Our life, as software, becomes more and more complex and wether we are able to do something in time or not, depends on a lot of systems and actions of different people. So, expect other to fail and plan enough time to get to airport, especially if you are living in place like London, with its crazy delays which, sometimes, caused by errors in somebody else software, too :).