Which leads back to this:
Let me see if I can simplify it: The sum of voltages around a loop equals zero. If you sum the voltages in the diagram you don't get zero you just get all the voltage drops. What is missing is the EMF source (the voltage rise) that produces these voltages across the resistors displayed.
I like this explanation the best so far, tells us what is going on yet is not too complex.
Think of the rise as a positive number and the drops as negative numbers. You could even place additional rises within the circuit and it still works out.
The impedance of the source is going to be a drop within the source, it will not be a fixed value like a resistor it will vary depending on the current.
And yes we run into this every time we calculate available fault current.