Yes, that's the trick.
> guess about how code works
That's not a bad thing per se. Time spent vs. accuracy is a compromise. You need to figure out what is the optimal depth of understanding you need to achieve to get the task done.
> copy and paste googled code
Sure, funderstanding code is usually much easier than writing it, so if you find something on SO that does exactly what you need then yes, just paste it.
> If I want to succeed, do I need to stop caring about solving problems and start caring about getting as many lines of code out the door as I can?
No, not at all. You should care about solving problems, but the problems you're trying to solve should more or less overlap with your employer's problems. If you are developing a trading system where the expected throughput is 10 trades/sec, then designing something that can cope with 1000 trades/sec might be interesting but it is not your job. If you need to fix some bug in 20 minutes because many things (money, reputation, etc.) depend on it, then yes, it might be just fine to guess, hack together something and fix it later properly instead of spending a couple of days on the 'correct' solution meanwhile the company is collapsing around you.
In short: what you do is part of a larger context, you need to align your priorities with that.