No, taking a quote of context is not the same as not running a quote with the source prior to publication. The former is unethical, the second is an optional practice.

I dont't run quotes by sources when I know that I have recorded it correctly and when I feel certain of the speaker's intent and context.

Most photojournalists don't let the subjects see the photos prior to publication. Not just in the past days of film, when it would have been logistically difficult, but even today with digital cameras. Most subjects have strong opinions about what photos capture them nicely. But photographers generally believe that photos capture truth, at least in a limited technical sense.

edit: It's worth throwing in a hypothetical cases based on real quotes. Pretend these happened in a private interview that you have taped:

- Case 1: "Rarely is the question asked, is our children learning?" [0]

If you were not a journalist sympathetic to President Bush, you would print this quote ad verbatim (minus the stutter before "is"), because it fits a narrative that Bush is a doofus, even when speaking about our children's education. I think if you ran this by him, Bush would politely request that "is" be changed to "are". But including the quote verbatim isn't a distortion of the truth, it's literally what's on tape.

- Case 2: "It depends on what the meaning of is is" [1]

Here's a case where a neutral reporter might ask for clarification, because the reporter is genuinely confused. However, I think most reporters would run with this, because even in a much longer interview/deposition, this quote seems to succinctly sum up Clinton's general shady evasiveness. Not sure what President Clinton would ask for here, he might have found it amusing to add to his Slick Willy persona.

- Case 3: "Reports that say that something hasn't happened are always interesting to me, because as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don't know we don't know." [2]

I personally think that this is a brilliant quote, on its immediate face. But it's such a complicated phrase that it's possible that maybe Secretary Rumsfeld messed up a syllable in such a way that totally changed the meaning. It does him nor the reader no good to leave in what was literally said if it doesn't represent Rumsfeld's mindset, unless the story is specifically about Rumsfeld's tongue twisters, and this is an example of how he tripped up.

So if you have a tape of the person speaking, and you are certain what they said, literally, and what they meant in context, what exactly is the point of reading the quote to them pre-publication, except to bring clarity in the cases where you are unsure? And what threshold of doubt does it become unethical not to offer a reading to the interview subject? It's not a clear decision, thus, why it's an optional practice left to the discretion of the reporter and circumstances.

[0] https://www.youtube.com/watch?v=-ej7ZEnjSeA

[1] https://www.youtube.com/watch?v=j4XT-l-_3y0

[2] https://www.youtube.com/watch?v=GiPe1OiKQuk