Something taken for granted might be something untrue. The left takes untrue things for granted all the time- makes assumptions that do not represent real life. A supposition- an assumption- is not a fact. The information or situation assumed may be true or may not be true.
Yes, something taken for granted may be untrue. But some things taken for granted—like my examples of the earth going around the sun or germs causing diseases—have lots of evidence supporting them. It’s why they’ve come to be taken for granted. Other assumptions might not have such evidence. It’s a common rhetorical technique to gloss over that difference, calling both things “assumptions” to make the former category seem as unsupported as the latter. It’s the same trick anti-evolutionists use with “theory” and “faith.”