everything I've heard and read suggests that there is no true random number generator. They are only pseudo random, so there is some pattern to their operation.

Well, all random number generators nowadays are based on input that's different each time. For example, most use the system time clock as a seed, which is a very large number when you take into account that it includes whatever the smallest increment of time the clock measures (which is going to be different depending on the chip and the code).

Agreed, that two pseudo-random numbers based on the same seed will produce the same output, but when the seed numbers are based on a time clock, (and the start trigger time is based on a human input like pressing the "go" button, or heck, even what time of day they choose to turn on the computer) you'll never be able to predict the output and it'll be different every time.

although I'm sure that is not what is causing everyone's aforementioned experiences.

Right, exactly. Whether the number is truly random or only pseudo-random doesn't apply to our discussion here.