Think of 'buy into' as metaphorically 'buying' or accepting an idea as you would purchase goods. She didn't just buy into the philosophy; she lived it.
Pro Tip 2/3
Emotional Investment
The phrase often implies emotional investment along with intellectual agreement. He bought into the dream of starting his own business with passion.
Pro Tip 3/3
Conversational Tone
Use 'buy into' in informal discussions when expressing agreement or belief. I buy into the idea that hard work pays off.