It depends on what he means by "leaking master cylinder"...
Within the master cylinder is a pair of pistons, which seal against the bore within the master cylinder block via rubber seals. Those seals wear out over time, particularly if the brake fluid is dirty.
So, if brake fluid is bypassing the pistons due to seal wear, you'll notice that the brake pedal doesn't feel like it has the same resistance as normal. In other words, when you press on the pedal, instead of a solid pressure the pedal continues to slowly sink towards the floor. However, that same sinking feeling can be caused by a leak in the brake lines, at the wheel cylinders, or where the brake line connects to the caliper. So I would check for leaks in those areas too. Usually, you'll get a brake warning light on the dash though, which it sounds like you aren't seeing.
Unfortunately, there's no master cylinder repair kit available for the LEAF, which typically includes new seals, springs, etc to rebuild the parts that typically wear out the fastest.
If the brake fluid leak is external, then it could be something as simple as a leaky cap on the master cylinder fluid reservoir. If that's the case, you'll likely find that if you top up the brake fluid then the fluid level will go down very slowly over a few months time. A replacement cap is less than $20, if that's what's leaking.
I would take your Leaf to an independent mechanic, explaining that Nissan says that the master cylinder needs to be replaced and that you want to confirm that's true.