the external surface of the leather would be ok with the water, however, the internal side would get wet and start to deteriorate. In other words, if you accidently dip in water a well made leather strap, there is a good chance that damages would be minimal if exposure is short and you dry it without using any strong method ( such as hair dryer etc...)
For the water resitance, you can trust JLC when they say that the watch is rated 30m, meaning that a differnce of pressure between the inside of the watch and the outside of 3 bars ( or equivalent to a depth of 30m in water) would not allow the water to enter.
hence, you could swim with your watch and it should be fine.
Now for scuba diving, this is clearly not an appropriate watch. Yes it is rated and tested for 30m, but one would want to trake a safety factor for the "just in case" and therefore nobody would dive with that type of watch.
the minimum for dive watches is 100m, for recreationnal scuba diving, which is usually limited down to 40m. that gives you an idea also of the safety factor that you may want to consider for your watches.
the watch industry started a race towards the biggest pressure rating possible for diver watches. in the early days of diver watches, 100m (300ft) was good enough. then we jumpted to 200m, 300m, 600m, and now, very commonly 1000m and occasionnally 2000m and up to 4000m for the recent rolex deep sea. Still, the human beings don't dive recreationnally much deeper now than when Cousteau and a bunch of french misfits invented scuba diving in the 50s.
summary:
don't immerse your leather strap on purpose in the water. It would suffer. accidental immresion should be ok if you dry it "slow"
you could swim with a 30m rated watch and it should be fine, but you increase the risk of problems and a problem like water intrusion in the watch will require a costly servicing of the watch
you can scuba dive with a watch rated 100m or more, provided it is of a reknwon brand that tests every watch and design and manufactures them seriously.
anything rated above 300m is an overkill, but, if teh watch can do "more" it can do "less" just fine as well.
last point: question the "pseudo" scietific evidence when people tell you that under the shower, the water that drops from the hose induces high pressure because it comes with "speed".
I hope this helps.