harry potter - Are Love Potions actually banned at Hogwarts?

Rita Skeeter's Witch Weekly article states that Love Potions are banned at Hogwarts.

Love Potions are of course banned at Hogwarts, and no doubt Albus Dumbledore will want to investigate these claims. In the meantime, Harry Potter's well-wishers must hope that, next time, he bestows his heart upon a worthier candidate.
_{(Goblet of Fire, Chapter 27, Padfoot Returns)}

Obviously Skeeter has been known to print the odd untruth in her time. I wonder if this one of them. There certainly seem to be plenty of Love Potion-brewers and -users at Hogwarts:

• Gilderoy Lockhart encourages students to ask Snape to brew a Love Potion for them.


• Molly Weasley brewed a Love Potion as a student.


• Romilda Vane repeatedly tries to dope Harry during Half-Blood Prince.


• Slughorn brews Amortentia, "the most powerful love potion in the world", in front of his sixth-year Potions class.


• The Weasley twins brew the "best range of love potions you'll find anywhere." These are banned by Filch along with the rest of the Weasleys' Wizard Wheezes products. Whether the Love Potions in that range were contraband on multiple counts is up for debate I think.

Pottermore only features this summary of the examples listed above. There's no JKR feature.

Are they actually banned? If so, why are they so commonly used with no disciplinary consequences? If not, why did Skeeter claim that they were as if it were obvious?

(Connected question. Note that I'm not asking about whether Love Potions were banned by the Ministry of Magic but whether they were banned at Hogwarts.)

Answer

Most likely that snippet is fact. The whole article that quote is from is a slam piece aimed at Hermione.

‘She’s really ugly,’ says Pansy Parkinson, a pretty and vivacious fourth-year student, ‘but she’d be well up to making a Love Potion, she’s quite brainy. I think that’s how she’s doing it.’

Here we have an accusation that we the readers know is a lie, but that many readers who don't know who Pansy or Hermione are could believe.

Next we have what I believe to be a piece of truth that all of her readers, as former Hogwarts students, should instantly see as a lie if it was not the case.

Love Potions are of course banned at Hogwarts, and no doubt Albus Dumbledore will want to investigate these claims.

She uses this truth to re-enforce the wrong-doings she claims Hermione is doing. Her whole article hinges on a piece of truth, which all of her readers would know personally, to back up the lies she perpetuates.