It really is interesting that our anecdotes can be so different. I'm assuming you're older than me (25) since you mention the pre-web internet, so I'd also guess that by the time you were on the web/pre-web internet you would've had a more developed filter than I.
My introduction to the web progressed roughly with watching my dad use BBS -> playing Neopets and Runescape -> becoming very involved with Runescape forums -> running a Runescape forum (first introduction to moderating user-submitted content at the age of 10. Yeah...) -> getting involved with video game modding communities, which meant I was spending all my free time browsing forums, following every link, completely absorbed by everything the early web's computer game communities churned out.
My experience probably would've been very different if I hadn't been able to get around the parental controls my parents used, or if I had been interested in different hobbies with a more approachable web presence.
I've been nostalgic for the "old web" lately, but I'm also very, very grateful that I haven't clicked on an inconspicuous URL that turned out to be a jumpscare, virus, weird porn, or gore in quite a while.
EDIT: I don't want to imply that the Disturbing Web == Videogame Web; that just happened to be my experience.