What if you find a permanently injured (broken leg, etc.) bird that is not of the three species you mentioned?
Call up a licensed rehabber. There’s usually one not too far away, no matter where you are.
I did that once. She gave me advice on care for the critter, told me that as long as I was working under her auspices, I was ‘covered’.
(I wouldn’t try this with something super-protected, though. And there are a lot of injuries/illnesses that the average person can’t manage. It’s best, then, to take them to a rehab place.)