these are the acts that have never had a top 20 ever apart from one No 1 hit.its worth noting that in britain the archies are the most successful 1 hit wonders as they spent 8 weeks at No 1 and 23 weeks in top 40,so christ knows where the TV show you mention got their info as its wrong.
1954: Kitty Kallen: Little Things Mean A Lot
1956: Dreamweavers: It's Almost Tomorrow
1958: Kalin Twins: When
1959: Jerry Keller: Here Comes Summer
1960: Ricky Valance: Tell Laura I Love Her
1962: B. Bumble & The Stingers: Nut Rocker
1966: Overlanders: Michelle
1968: Crazy World Of Arthur Brown: Fire
1969: Zager & Evans: In The Year 2525
1969: Jane Birkin & Serge Gainsbourg: Je T'aime... Moi Non Plus
1969: Archies: Sugar Sugar
1970: Lee Marvin: Wand'rin' Star
1970: Norman Greenbaum: Spirit In The Sky
1970: Matthew's Southern Comfort: Woodstock
1971: Clive Dunn: Grandad
1973: Simon Park Orchestra: Eye Level
1975: Typically Tropical: Barbados
1976: J.J. Barrie: No Charge
1977: Floaters: Float On
1978: Althia & Donna: Uptown Top Ranking
1978: Brian & Michael: Matchstalk Men & Matchstalk Cats & Dogs
1979: Anita Ward: Ring My Bell
1979: Lena Martell: One Day At A Time
1980: Fern Kinney: Together We Are Beautiful
1980: M*A*S*H Theme From Mash
1980: St. Winifred's School Choir: There's No One Quite Like Grandma
1981: Joe Dolce: Shaddap You Face
1982: Charlene: I've Never Been To Me
1985: Phyllis Nelson: Move Closer
1987: Steve "Silk" Hurley: Jack Your Body
1987: M/A/R/R/S: Pump Up The Volume
1988: Robin Beck: The First Time
1990: Partners In Kryme: Turtle Power
1991: Hale & Pace: The Stonk
1994: Doop: Doop
1996: Dunblane: Knockin' On Heaven's Door
1997: Teletubbies: Teletubbies Say Eh-oh!
1998: Chef Chocolate: Salty Balls
1999: Mr. Oizo: Flat Beat
1999: Baz Luhrmann: Everybody's Free (To Wear Sunscreen)
2000: Black Legend: You See The Trouble With Me
2000: Spiller: Groovejet
2000: Rui da Silva: Touch Me
2001: DJ Pied Piper: Do You Really Like It
2002: Las Ketchup: The Ketchup Song (Asereje)
2003: Tomcraft: Loneliness
2003: Michael Andrews feat. Gary Jules: Mad World
2004: Frankee: F.U.R.B (F U Right Back)
2004: 3 Of A Kind: Babycakes
2004: Eric Prydz: Call On Me. . . 50th One Hit Wonder
2005 Steve Brookstein - Against All Odds
2005: Nizlopi - The JCB Song
2006: Chico - It's Chico Time
2006: Orson - No Tomorrow
2006: Ne-Yo - So Sick
2006: Gnarls Barkley - Crazy