Is there any difference in the protection from a GFCI outlet vs. a secondary outlet connected to it?
"Inspector" is not too swift - I'd be tempted to run this up to the organization that certifies them as a qualified inspector, but I do like to make trouble sometimes.

They don't care at all about a short line to neutral - that's the circuit breaker's job. What they do is compare the current going on the line and the current coming on the neutral, and if they are not matched within 5 mA (number varies with part of world, but for the US) they trip - that happens when there's a fault (often far less than a full on short) to ground.

They work exactly as fast for remote or local connections, as they measure the current, and current changes instantaneously throughout a circuit with changes in load.

Some people even prefer GFCI breakers, which are all the way back at the panel. They work just as well.