I would never use those to write something important in a notebook. I did this and left it in my bag, the sun shone on the bag and because of the heat most of my notes got erased. Well because friction = heat, so it was the same thing.
(pilot frixion, blue, bought in Norway)
But if I were in uni or something and were forced to maintain multiple projects at the same time(modules) I would probably opt for something else.
Ball-point pens don't feel the same, and the colors don't stand out as much to me. I've accepted the fact that water is a dangerous thing to my notes now.
Water based != water soluble when dry
I would suggest you try similar pens with a different ink. Staedtler Pigment Liner and Sakura Pigma Micron pens (both of which come in 0.3 mm) use water based pigments which are waterproof when dry and archival. They both survive rain quite well in my experience and are used for outlining by some artists who then apply water color paints or other water based media without the dried ink bleeding.
There are also waterproof fountain pen inks. Platinum Carbon and Noodler's Bulletproof Black are two good ones.
For a common counter example to a water based substance being water soluble once dry consider water based exterior latex paint.
Unfortunately every pen of this kind I've used suffered from being water soluble after dry, so I just assumed all where.