On the first point, big companies clearly feel that they can claim any project that is related to the company's lines of work, not yours.
Companies like Google, Amazon, and Microsoft have arms for hardware design, video game development, web development, close-to-the-metal graphical programming, embedded systems, retail...that's not just big enough to drive a truck through, it's big enough for that platform they truck space shuttles around on!
You can say that those companies are unlikely to realistically claim ownership of anything that YOU didn't work closely with, but I can say from experience that these companies have explicit company-wide policies regarding some of those areas, with stricter mandatory reporting guidelines, and even requirements to use that company's technology, separate from their ordinary side project/open source contribution/etc. policies.
So I wholeheartedly agree with your second point - what you do off the clock is none of your employer's business, full stop. Just don't use company equipment for it.
When I was there I submitted three, every time they came back and said that they wouldn't sign off because it was related. The last one was an iOS only kitchen timer application.
It was at that point I was was convinced that emailing legal to ask permission was a hack to get you to disclose early what you were working on so that when they sued you they already had some of the initial leg work done :-(.
I consulted with an attorney on this and they advised me that because I was working in California the burden of proof that it was related to Google's business was on Google. But that in his experience they were not above pushing the edge of the definition. The bigger point though was that people don't work at companies that are suing them and generally don't work at any company if they have a reputation (real or imagined) of doing work on their own time that is "against" their employers interest.
The summary of his advice was never, under any circumstances, work on any project you don't want to give Google ownership of while you are employed there. And when you have an idea that you want to develop, quit so that those parts of your employment agreement are nullified.
They can still come after you if they think you are using "proprietary or confidential" information in your new effort but that is less common and it makes them look like the bad guys not you.
Google has a painless and usually very fast process for this. It's done on a project by project basis and gives the developer a certain amount of peace of mind. There is a separate process for non OSS work as well. Or at least there was when I was there a couple of years ago.
I never had any problem getting the ok but everyone's experience will be different depending on a number of factors. It's useful to know up front either way though.
This seems insane. I make tiny pull requests all of the time - sometimes it's just a documentation typo fix! If you're a Google, you need to send those through a lawyer, or you'll (I assume) get fired? Ignoring the intrusion, that's a good use of Google's expensive lawyer time?
I will be starting at the job the next summer (graduating next summer) and I too thought the same. If I didn't use the company's infrastructure or their internal technology or do the work while on company time (9 to 5) - then they should not be able to claim my work.
TL;DR If you could not have built the product without being an employee of the company, it probably belongs to them.
eg. Maybe you use Microsoft's latest internal only HoloLens prototype to build a product. You couldn't have done that if you weren't a MS employee - so they can claim it.
But if you used the dev kit and publicly available tech and features then they shouldn't be able to claim it.
Companies like Google, Amazon, and Microsoft have arms for hardware design, video game development, web development, close-to-the-metal graphical programming, embedded systems, retail...that's not just big enough to drive a truck through, it's big enough for that platform they truck space shuttles around on!
You can say that those companies are unlikely to realistically claim ownership of anything that YOU didn't work closely with, but I can say from experience that these companies have explicit company-wide policies regarding some of those areas, with stricter mandatory reporting guidelines, and even requirements to use that company's technology, separate from their ordinary side project/open source contribution/etc. policies.
So I wholeheartedly agree with your second point - what you do off the clock is none of your employer's business, full stop. Just don't use company equipment for it.