I think that comes down to your desire to learn. One person might just repeat a google answer but another person might spend some time thinking about why it's the right answer.
Google is how people get degrees after all, it's the modern day version of hunting down books in libraries
I get what you're saying about how people establish stronger pathways when they discover something on their own rather than copying something down but at the same time, that's how education works. You have something explained to you simply first, whether that's by human instruction like a prof or written instruction/visual demonstration like doing your own research on google. Of course there are low quality/high quality internet sources just like there are low quality/high quality professors and that goes back to how much of a desire the student has to learn, whether they just want to copy and paste answers or actually understand why it is that answer.
As a math teacher I'm sure you can agree that high level academics depends on having a understanding of the fundamentals. If I don't understand algebra or polynomials then It's going to take me a while to get a hang of derivatives or calculus and that doesn't mean I'm stupid or lazy, I just haven't devoted my life to that specific field because I have 9 other courses to study at the same time. Graduation numbers would be insanely low if we expected kids to figure everything out on their own without access to previous knowledge like the internet. Having the world's library at your fingertips gives you the ability to copy and paste but also the ability to be an autodidact, it really depends on that specific person's desire and goals.
I had a lot of foreign students as TA's for my calc courses, I know it's not their fault but it was really difficult for a lot of us to understand their accents and we didn't want to be rude by asking them to repeat themselves all the time. If I didn't learn google-fu for explanations on concepts I would have failed those classes easily.