Please note that the caveats are with a flat-sided, well fitting, dry yoke dust cap.
Alec saved my regs (at least) once. During my first LDS trip to Cozumel many years ago, I was chatting away after a night dive. I thought I had already put the dust cap on and started putting my regs into the rinse tank and realized the cap wasn't on and pulled them out right away. The DM said, they'll be ok, let me dry them.
He proceeded to blow them with a tank, and I immediately thought, "uh oh, Alec said not to do that because if you don't do it properly, the water will be pushed further in". He said, "they'll be fine".
After getting home, I took them to Alec for service but didn't say anything about the uncovered dunking. He called me a couple of hours later to tell me that there was a little salt water right through into my (analog) gauges. He said I was lucky I brought them right away because he was able to clean and dry them out, and if I had waited, they would have corroded. Alec was widely considered one of the best reg techs in Ontario.
After that I was really careful about having the dust cap on and still soaked it as I had been taught in my o/w course. Fast forward 17 years to my last liveaboard and someone told me that I shouldn't soak the first stage, and especially not in the rinse tank as there could be lubricants from other people's stuff that could degrade the o-rings in my regs.
Ok, so combined with the potential of forgetting to cap it or not having a good seal, I stopped soaking the first stage after salt water and rinsed it well with the regs still on the tank, if possible. At home, I rinse the 1st and 2nd stages and then soak only the 2nd stages.
I'm suddenly glad that most of my dives are fresh water.