I don't agree with the answer.
Fill factor is available for viewing in the view (?) sys.indexes. It would probably be a bad feature for reorgs to ignore the "set" fillfactor (you know, the entity that this question assumes does not exist), and additionally, you cannot specify fill factor for reorgs. So lets do a thought process here, say you rebuilt an index with an SQL statement that specified a fill factor of 75. If this setting were not persistant, what would the next reorg use? 100?
Think about it, if I set the fill factor to 75, then did reorgs later that subsequently used a fill factor of 100 because according to the OP the fill factor doesn't persist, wouldn't that just make reorg a pain to use?
What this question seems to muddle is that there is a "specified" fill factor that you can examine for each index in the view sys.indexes, an actual empty space percentage for each page of the index at a specific point in time, and average empty space percentage for the entire index at a specific point in time.
We know pages fill up then split when inserted (obviously not at the very last index leaf for sequentially increasing index key values, these probably don't need splitting, we just get a new page), but this question seems to imply that the fill factor is not persisted anywhere and I just don't think this is accurate.
This page https://www.brentozar.com/archive/2013/04/five-things-about-fillfactor/ seems to back this up:
Once fillfactor is set on an index, it stays there. Further rebuilds or reorganizations of the index maintain that fillfactor unless you specify a different value. It’s easy for a change in fillfactor to sneak in. Unless you check for indexes with a fillfactor set, you might not realize what’s going on in your database.