The Plant Explorers site (with its nice picture) expresses the author's scepticism about the gardens in a fairly typical way. There are two components:
We have seen that the gardens were documented by Ctesias, c.400 BC—long before Alexander and his troops went to Babylon in 331 BC. So we need not waste time with the troops. But the poets may be important, and they are maddeningly elusive. Several intensive web searches produced two rather weak allusions online:
Eventually I also found a 19th-century poem, which is pasted at the bottom of this page. That poem has a lot to tell us about the time in which it was written, but it has nothing to do with those "Greek poets".
So what is going on with those poets?
One possibility is that we have not only lost all those poems in the 2000+ years since they were written, but that we have also lost all reference to them. That may be the case, but it would be feeble to make that assumption without checking out every other possibility first.
Another possibility is that we do have the poems, but they are no longer well enough known to make it to the web. So we may need to consult a Classics professor somewhere.
Clayton and Price include a chapter by Irving Finkel, who provides a longer extract of Quintus Curtius than you can find on the web. In Finkel's rather vicious translation, Quintus Curtius comments that the gardens are "a trite theme with the Greek poets". The translation from the Livius site goes like this: a wonder celebrated by the fables of the Greeks".
This is a very commonly used book, so it is probably the reason so many people mention those Greek poets. But who were the poets, and what did they say? Finkel doesn't tell us.
Fortunately, at the front of the book, there is a poem by Antipator of Sidon, written c.150 BC. This happens to be the ealiest surviving list of the Seven Wonders of the World (although you'll see that he does not call them that).
A web search for this poet indeed produced the poem in a malfunctioning website that had not otherwise made it into the search engines. Here is the poem:
I have gazed on the walls of impregnable Babylon,
along which chariots may race,
and on the Zeus by the banks of Alphaeus.
I have seen the Hanging Gardens and the Colossos of Helios,
the great man-made mountains of the lofty pyramids,
and the gigantic tomb of Maussollos.
But when I saw the sacred house of Artemis that towers to the clouds, the others were placed in the shade, for the sun himself has never looked upon its equal outside Olympus.
Clearly, this poem alone could never support the idea that the Hanging Gardens only existed in the minds of Greek poets—much less that it was a "trite theme" (i.e. repeated to the point of boringness). So what gives, here?
If the Greek poets never existed outside Finkel's translator's imagination (which we have yet to verify), the reference to Greek interest in the gardens remains valid.
It appears as a side comment, dropped rather abruptly into Clitarchus' text, which is otherwise wholly concerned with description. As it stands, it is an odd comment for Clitarchus to have made, since he was Greek himself. But it would make sense for a non-Greek, such as Quintus Curtius Rufus—who was Roman—or some later copyist, to add the comment, possibly as a glossary note above the text. Why would he do that?
Quintus Curtius never directly says who built the gardens. He could hardly do so without disrupting the truth hierarchy. But we have seen that Ctesias, Clitarchus, Diodorus and Strabo all discussed them in detail; as did Philo of Byzantium (if it was him, and if he was Greek). So the theme was indeed well-known among Greek writers, all of whom either attributed the gardens to Semiramis or preserved a diplomatic silence. Like them, Quintus Curtius sets the garden description in the middle of an account of Semiramis' building achievements. He preserves his own diplomatic silence but by reminding us of Greek writers, and by copying their narrative strategy, Quintus Curtius could take a side on the issue without appearing to do so.
BE still. The Hanging Gardens were a dream
That over Persian roses flew to kiss
The curlèd lashes of Semiramis.
Troy never was, nor green Skamander stream.
Provence and Troubadour are merest lies
The glorious hair of Venice was a beam
Made within Titian's eye. The sunsets seem,
The world is very old and nothing is.
Be still. Thou foolish thing, thou canst not wake,
Nor thy tears wedge thy soldered lids apart,
But patter in the darkness of thy heart.
Thy brain is plagued. Thou art a frighted owl
Blind with the light of life thou'ldst not forsake,
And Error loves and nourishes thy soul.
—Composed 1898, published 1902.