In a "big company you've absolutely heard of" it can be very hard to claim that you are outside of your employer's market. Several such big companies define their market as "everything tech-related".

(Whether this would stand up in court is dubious, but do you also want to go up against a billion-dollar company's crack legal team in court?)

Also, I've heard the main issue isn't actually getting sued, it's that VCs or investors won't even touch you if there's the slightest hint that you might not own your code. If your side-project takes off it's nice to be able to enlist other peoples' help instead of miring yourself in legalities.