This is incorrect, I believe. Almost all airlines have a small open closet between the first class and coach class sections which contains a rack specifically for hanging suits and blazers.
It is mainly designed for first class section. If you hang your suit there, the steward/ess will not care though, although if you voluntarily ask them they might disapprove. I advise choosing a airline seat closer to the front, in case something happens to it (Someone could potentially grab it while exiting the plane).
The only caveat is that for short flights (props or little jets) this feature does not exist; although you may be able to sweettalk the steward/ess into letting you use the stocks closet. Since little flights tend to be more spare, you will also probably be able to drape it over the empty seat next to you or in front of you.
Another side note for professional/business flights: Since you probably have carry-on, try to avoid boarding the plane late, to get a good overheard spot nearby your seat. If you are doing red-eyes, bring sleeping pills, ear plugs, and eye shades. Red-eyes are actually the most difficult flights to sleep on, because families use them to save money. Plan out aspects of your flight (food to bring, water bottle, reading material) so you feel refreshed and rejuvenated when you step out of the airport, vs. weary and frazzled. Don't stampede to reach the baggage claim, no one will bother with your luggage unless you have matching Italian leather cases; and it takes about 20 minutes to be unloaded anyway.
