You mentioned Shared Calenders. The default reminder option is for your defualt calender only. The second thing you mentioned is

"On other peoples computer by unchecking the "default reminders" box we get the "none" setting in the new appointment"

if you are creating an appointment on a shared calender, the calender settings are those of that defaulted user. If there option is set to none then the calender reminder will be set to none by default.

My question is, the calender you are setting this appointment/reminder on is it a shared calender? or a Second calender that you are the owner of?

Best Regards,