While most offering plans are largely boilerplate, this is one of the few areas that can be particularly different. There is often some language about the definition of "apartment" and "outdoor areas appurtenant there too." There have also been a number of lawsuits over these definitions (ex
https://sgrlaw.com/articles/yet-ano...-93rd-st-over-deck-space-next-to-greenhouses/).
There have also been lawsuits when there was no question the Offering Plan allocated an outdoor area to a unit but for some reason the Coop Board/Managing Agent determined the use should be curtailed, or decided to change the rules of use (ex
https://therealdeal.com/2020/05/28/sutton-place-co-op-in-turmoil-over-terrace-fees/ ) or revoke permissions (ex
https://www.habitatmag.com/Publicat...21-June/Enclosed-Balconies-May-Not-Be-Forever).
If the managing agent/Board is telling you the unit has no terrace and the offering plan is silent you are really taking your chances that at any time you can be told to stop using it.
I agree with Noah that if it doesn't look like there have been extra shares allocated it's harder to show an intent of the Offering Plan to grant the unit extra space. Same if other units under the same Offering Plan are designated with any notation (such as "T," "G," "Ph," etc) and this one isn't.
None of the above should be taken to construe that I'm not aware of similar situations where unit owners have been allowed to use such spaces without incident for long periods of time. Also the same where after using them for long periods something came up and all of a sudden it became an issue.
Question: did the current unit owner improve the area in some way and use it "openly and notoriously"?