Neither of those things are cyber stalking.
The principal element in the first scenario is a stalker, not a cyber stalker. Stalking pre-dates the internet, and the only thing (which you don't even make clear in that scenario) is that the threats come over an online medium, rather than over phone or mail or in person.
The second scenario is exactly the same. With or without the internet, lurid allegations can be spread within a community leading to the same issues.
i don't think you will find anyone arguing that stalking is not bad, but this is specifically about cyber stalking - and cyber stalking is nonsense:
Someone keeps emailing you? Shit list them
Someone keeps IMing you? Shit list them
Someone keeps pestering you on forums you frequent? Ignore them
Once it stops being cyber stalking, and becomes actual stalking, like the examples you provide, then it is an issue. Cyber stalking is not. The internet pervades every aspect of life these days, and characterizing 'stalking which uses the internet as a communication medium' as cyber stalking does you no justice.