With all due respect, I am sorry to say, you are not correct. Termites do bit, you may not feel it right away, and yes it is very rare; nonetheless, they will and do bit.
Logically, most every living thing tries to protect itself, family, and its space. Though small, when they spawn and you do not know what to think, because you are fighting a bunch of winged bugs (look like flying ants), that do not stop coming, you are bound to be bitten at least once or twice. I do not have spiders, mites, lice, fleas, or mosquitos. I respect all professional; however, just because you have not heard of it or experienced it, does not mean it is not so. They I do not know if they have good sight or not, I do know that it has happened, it is real, and they hurt as they heal. Their bits are very different from any other flying or crawling pest, during the healing process. Yes, at first the bit looks like little pricks, or a small mosquito bit, maybe even a bedbug, flea, mite, or lice bite, but, as they heal they come together and form something like a blister of sorts in the form of a shape. I know this sounds crazy; nevertheless, it is true, it is real, it hurts, and it takes more than two-weeks to heal.
Personal experience, never seen an termite before a-day in my life (up-close-n-personal that is), was able to capture one after the third hatching. Myself and my daughter were bitten, Landlord tried to tell me differently, Doc and profesional says, it does happen, however, rare.