The network of contacts you make through university and your careers is a mechanism by which you hear about jobs you might otherwise never get the chance to apply for. That’s a very real thing, but will tend to be dominated by contacts you make after university as your career progresses.
The other thing of needed a degree from a particular university, or a PhD, isn’t so much about a network as that degree being a shibboleth. The person reading your job application sees that and knows there are questions they don’t need to ask.
These are both things you can, and may need to, work around if you go down the self taught route. Depending on the work you want to do you may need to make sure you do work which either you can point to or other people will see so that you hear about those jobs, or get a referral to avoid the normal job requirements.