It's not a silly question.
"Precum" is a fluid that comes out of a guy when he gets an erection. It's produced by the Cowper's gland, and has no sperm in it at the beginning.
But if the guy has recently ejaculated (and the jury is out on how recently that has to be), there might be living sperm from that recent ejaculation hanging around in his urethra. Since the fluid from the Cowper's gland is body temperature and is travelling through the urethra on its way to ooze out when the guy gets an erection, some of those sperm can hitch a ride in the pre-ejaculatory fluid. So yes, "pre-cum" can contain viable sperm. That is the "reason that chances still exist" that you're freaking out about.
The folk wisdom is that if the guy pees before getting the second erection, it will wash out his urethra and there won't be sperm in it from the first erection and ejaculation. While peeing doubtless has a washing-out-the-urethra effect, I don't know how perfectly it does that, especially if you only peed one time and the ejaculation before that was relatively recent. I think in your position I would never rely on one time peeing after a recent ejaculation to remove all sperm. When a guy ejaculates, he produces about a teaspoon of semen (between 2 and 5 mililiters) and in each ml there are normally about 100 million sperm. Heck of a lot of sperm, one time peeing might miss a few.
So yes, as your reading is showing you, it's rare to get a girl pregnant that way. But this is a lot of the explanation for why having unprotected sex and "pulling out" can't be relied on to prevent pregnancy. There are so incredibly many sperm in an ejaculation, and who knows if the Cowper's gland fluid found some on the way out.
Try not to worry, you probably didn't get this particular person pregnant this particular time -- it isn't the easiest way to get someone pregnant. But unprotected sex is going to get someone pregnant sometime, and you really don't want that to happen when you are just having recreational sex. God invented condoms for a reason. Don't be casual about that. :-)