[W]hen you ask your boss if online engineering coursework is good for getting a new job, they would tell you "you're fired".
Maybe in Corporate America, where you have to slave 60 hours a week just to keep your job, and where you're expected to feel guilty for wanting to have a social life. In Europe (at least developing software in the Netherlands), this is simply not true. The reason: employers realise that a high turnover costs a huge amount of money and worse, delays projects. The latter costs time to market, which can be even more expensive and in extreme cases can kill the company.
To be fair, some employers do cover furthering education, but again, usually it cannot come at a cost to your already full workload.
This is true. It is also the reason why your education, even if paid by your employer, is done in your personal time (usually partially for mandated courses). This way both you and your employer invest, which is only fair.