That particular example was supposed to demonstrate that having a bachelor or master degree (or even PhD) does not necessarily prove you have a hs diploma. There is no logic behind.I was admitted to college after only 3 years in Hight School ( in Europe). I got my BS degree and went to school again after I moved to US. My college in US only asked for my transkripts and my college diploma. The US recognazed and applied credits of all of my liberal arts classes so I was only studying majors.
So, yes you can go to college without HS diploma and yes it shouldn't be a problem for anyone who got and can prove higher education acquired in a meantime.
At the same time, requirements to hs education include an important requirement that you could be admitted to ANY university based on your education, not to just one particular university.