(it says it includes all random events)
It doesn't. The problem with using a bot that doesn't have failsafes for randoms it cannot solve (being almost every injection/reflection bot) is that if it gets in a random it cannot solve, it will usually fuck around and fuck up in loops until Jagex force logs it out @ the 6 hour refresh feature, or you stop it yourself.
RiD and Simba both will solve the randoms that it can, and for the ones it cannot, it will log out, meaning there's no risks to your account related to random events. The worst that could happen is you get the prison pete random, log out, and don't solve it within 15 minutes, which automatically makes you fail Prison Pete (not the others). This doesn't effect your chance of ban, however it does make it so that you will be getting randoms a lot more often.
Random frequency is based on the number of solved randoms in a row, experience gains, and if you recently failed a random or not.
The more randoms you solve in a row, the less often you will get them
If you fail a random, you will get them more often
You will get a random after X experience has been earned, regardless of the activity. If you are using a bot that gains lots of experience quickly in an area that gets randoms, you will get the randoms more frequently. Every time you solve a random, you will get the next random after X + Y. X is the previous experience gained before you got the random, and Y is an unknown number that Jagex's systems automatically choose. This means, for example, if you got a random after ~300k exp, your next random would be sometimes after 300k exp. If you are solving randoms successfully, you will not get a random after less exp than was gained before getting your last one.
If you fail a random event: Let's say you're up to ~400k exp before you got a random. Then let's say you failed the next random you bot. It is likely our exp needed counter will drop heavily. Most of the time I fail a random I get my next 1-3 randoms after ~70-80k exp, and then after that it usually goes up.