The Hindemith
Symphonic Dances come close to being an untitled symphony as well, with an introduction and fugue, a scherzo, slow movement and finale, although this was something Hindemith did frequently (likewise in the Symphonic Metamorphosis, and there's no particular reason the Concerto for Orchestra is called that instead of a symphony either, or for that matter the two Sinfoniettas; Hindemith
was uncomfortable with the title of symphony, despite writing six officially titled ones). But apart from Hindemith and Rachmaninov, the Grieg—and almost every subsequent set of "symphonic dances" I can think of—puts a lot more emphasis on the "dance" part. You can't very easily dance to the Rachmaninov Symphonic Dances.
That doesn't make it a symphony, of course. Just some additional context. Rachmaninov may or may not have known or cared much about the Hindemith example (although it was much more recent), but he almost certainly would have known the Grieg, and perhaps the two freestanding sets of "dances" by Kodály, among others. There was a rather common fashion in the early 20th century for writing "dance suites" (that may or may not have been particularly danceable) for orchestra. So "dance" had become almost completely divorced from actual dancing by this point, with freestanding suites not based on any kind of ballet or similar theatre work, and "symphonic" was also in the process of divorce from the idea of the symphony per se, with symphonic works now arguably being any piece for large orchestra.
