Appleton deleted the message, but told BuzzFeed that the message had come from Richardson's Facebook page.
Later, Appleton tweeted: "Beginning to wish I hadn't posted that… it doesn't matter who you are or what the industry is, just be a decent human being."
She added: "The fact people think this is acceptable blows my [f**king] mind. See ya."
Appleton then deleted her Twitter account.
Richardson's spokesperson Candice Marks told BuzzFeed, "This is obviously a fake. Terry did not send this text."
After the allegations were made, and media inquiries were presented, Vogue U.S.'s communications director Hildy Kuryk released a statement saying, "We have no plans to work with [Richardson] in the future."
It was also made clear that the last time the 48-year-old photographer worked for Vogue U.S. was in 2010. However, Richardson has worked with French Vogue earlier this year.
Richardson is one of the most high-profile fashion photographers currently working in the industry. Aside from his many magazine shoots, he is also a music video director, creating the controversial but hugely popular video for Miley Cyrus' Wrecking Ball, as well as the video for Beyonce's XO and Taylor Swift's The Last Time.
Richardson has been the subject of accusations of sexual impropriety in the past. Model Charlotte Waters accused Richardson in March of making inappropriate and unwanted sexual advances towards her, as well as a number of other models in the past. The accusations were made on the website Reddit. Initially, they were made anonymously, but Waters later came forward.
"…Enabled and protected by the freewheeling and often times anonymous nature of the Internet, people have become comfortable concocting hate-filled and libelous tales about my professional and personal lives. In writing this, I make a humble attempt at correcting these rumors, because I have come to realize that absent my voice in the conversation, all that remain are the lies…
"…Like Robert Mapplethorpe, Helmut Newton, and so many others before me, sexual imagery has always been a part of my photography…I have never used an offer of work or a threat of rebuke to coerce someone into something that they did not want to do. I give everyone that I work with enough respect to view them as having ownership of their free will and making their decisions accordingly, and as such, it has been difficult to see myself as a target of revisionist history. Sadly, in the on-going quest for controversy-generated page views, sloppy journalism fueled by sensationalized, malicious, and manipulative recountings of this work has given rise to angry Internet crusades. Well-intentioned or not, they are based on lies…"
"…Over the course of my career, I have come to accept that some of my more provocative work courts controversy, and as an artist, I value the discourse that arises from this. I can only hope for this discourse to be informed by fact, so that whether you love my work or hate it, you give it, and me, the benefit of the truth."