Sorry for the confusion.This is the specific answer to the original question. It suggests that your MCB is single-pole (some European installations use SPSN or DP MCBs) and only disconnects the line. When the short occurs, there is a path through any other loads for a small current driven by a small difference in voltage between neutral and earth, tripping the RCD. That voltage is too low to be detected with the handheld tester.
What was confusing was your comment that 'fuses blow when...' Normally we wouldn't use that description for an RCD trip because the MCB is equivalent to a fuse, not the RCD, and any short that trips an MCB tends to create a bang!
Does the RCD trip because it detects a slight current going to the ground? because it says 63 Amps on it.