For the covered call, getting assigned isn't so bad if your strike is above the price of the UL. It's not a realized loss, but it is a lost opportunity to have sold the UL for a higher profit if the UL stock price goes above strike + call premium. However, as the call writer, you are not in control of what happens. Sometimes you want to get assigned to get rid of the shares, and sometimes you would prefer to hold the shares and collect the call premium for extra income. Either way, it would help a lot to have some tool to be able to figure out those odds of early assignment, to see which one is more likely to occur. For a cash-covered put, it is a more problematic issue - getting assigned (early or not) means you now own shares at a price below the strike price. You may have an unrealized loss if the UL moves below strike + put premium.
I can't say for sure but I can speculate. Since they don't really coach naked calls (considered too risky) I feel confident the conversation was regarding selling naked puts. As to the time frame, they generally teach entering an option position 30-45 days out.
Don't get hung up on the "odds" of early assignment. If you're a CC call writer, early assignment is a good thing because you don't have to wait as long (exp) for that maximum profit. If you're a NP writer, getting assigned while OTM is a good thing but very unlikely to happen. If assigned early because ITM, the assignment didn't cause the problem. Going ITM did. A potentially serious problem with NP's at expiration is pin risk where the UL is hovering near the strike. If assigned, you may end up with shares whose price can move before the next trding day. That can be a good thing if in your direction, bad if not.