Hello Edw-partscaster,
I assumed the comment on using a strap was intended to be a lesson on good body posture while playing. There are lots of ways to sit or stand while playing the guitar. Any of them should work fine as long as you are comfortable and you enjoy playing that way. Where the strap suggestion fits in for me is that it helps considerably to hold the guitar in a comfortable position while using a strap.
Personally I switch between many different body positions while playing. Standing while using a strap, sitting (with or without strap), guitar placed on right leg or left (depending on the type of chair I am in). What I have noticed works best for me is when I am in a position that has the guitar neck slightly upright, so that my fret hand is raised a few inches higher than my pick hand. When I play sitting with my acoustic I guess this would be called more of a "classical style" posture (instead of the "rock style" posture that holds the guitar nearly parallel to the floor).
When I play electric I use the strap always, no matter if I am sitting or standing. This is recent for me and I think it helps. The strap makes it easier for me to hold the guitar at the angle I prefer, and allows more range of movement for my left hand. Also seems to help with wrist tension when I have the neck higher, which makes it more comfortable to play for longer.
So to really answer your question of "Big mistake?" I would say, no, it is not a mistake on your part. If you are playing comfortably and you like how it feels to hold the guitar in your hands that way, it seems like it is working for you. But if you notice any strain or physical discomfort then please stop playing right away and either take a break or try to figure out if there might be a more comfortable way to hold the instrument.
I hope this helps!