Daylia, et al, YES!! Most of the time, when a person hears normally & has normal vocal function, it is a matter of education. I, also, have taught persons who were "tone deaf," "couldn't carry a tune in a bucket," etc. to match pitch & sing well.
    I have noticed a trend in recent decades, that more of our children are less able to match pitch than years back. I believe that the old ways of teaching elementary teachers & Music teachers were better when it comes to pitch. There was more emphasis on singing & singing games without recordings or electronics. Solfege (do-re-mi) was the norm.
I also have known many people who were told by an alleged "music teacher" that they could not sing. As a Music Educator, I would NEVER do this. Instead, I say, "We can all sing!" I would challenge the those alleged teachers to take it upon themselves to dig out their class notes & textbooks, call their music ed profs, take some more elem music classes & learn how to effectively teach pitch.
As to "perfect pitch," how does the stork know which child born with "perfect pitch" to drop in the USA where we use A=440, & which child to drop in another country where they use A=438, & which child to drop off in a country which has semi-tonal based Music? Is it nature, or is it nurture?