Question: Are both Lambert Hillyer and Charles Shyer American film directors?

Context articles: Chain Lightning (1927 film)
The Whistle (1921 film)
The Money Corral
Travelin' On (film)
Lambert Hillyer
Charles Shyer
The Cradle of Courage
Square Deal Sanderson
The Testing Block
The Branded Sombrero

Chain Lightning is a 1927 American silent Western film directed by Lambert Hillyer and written by Lambert Hillyer and Malcolm Stuart Boylan.
 The film stars Buck Jones, Diane Ellis, Ted McNamara, Jack Baston, William Welsh and Martin Faust.
 The film was released on August 14, 1927, by Fox Film Corporation.
The Whistle is a 1921 American silent drama film directed by Lambert Hillyer and written by May Wilmoth, Olin Lyman and Lambert Hillyer.
 The film stars William S. Hart, Frank Brownlee, Myrtle Stedman, Georgie Stone, Will Jim Hatton, and Richard Headrick.
 The film was released in April 1921, by Paramount Pictures.
 A print of the film is in the Library of Congress.
The Money Corral is a 1919 American silent adventure film directed by Lambert Hillyer and written by William S. Hart and Lambert Hillyer.
 The film stars William S. Hart, Jane Novak, Herschel Mayall, Winter Hall, Rhea Mitchell, and Patricia Palmer.
 The film was released on April 20, 1919, by Paramount Pictures.
 It is not known whether the film currently survives, and it may be a lost film.
Travelin' On is a 1922 American silent Western film directed by Lambert Hillyer and written by William S. Hart and Lambert Hillyer.
 The film stars William S. Hart, James Farley, Ethel Grey Terry, Brinsley Shaw, Mary Jane Irving, Bob Kortman, and Willis Marks.
 The film was released on March 5, 1922, by Paramount Pictures.
 A copy of the film is in the Library of Congress.
Lambert Harwood Hillyer (July 8, 1893 – July 5, 1969) was an American film director and screenwriter.
Charles Richard Shyer (born October 11, 1941) is an American film director, screenwriter and producer.
 Shyer's films are predominantly comedies, often with a romantic-comedy overtone.
 His films include "Private Benjamin" (1980); "Irreconcilable Differences" (1984); "Baby Boom" (1987); "Father of the Bride" (1991); and "Father of the Bride Part II" (1995), "The Parent Trap" (1998), "The Affair of the Necklace" ("L'Affaire du Collier") (2001), "Alfie" (2004) and "Ieri, Oggi Domani (Yesterday, Today and Tomorrow)" (2012).
The Cradle of Courage is a 1920 American silent drama film directed by Lambert Hillyer and written by Frederick Bradbury and Lambert Hillyer.
 The film stars William S. Hart, Ann Little, Tom Santschi, Gertrude Claire, Frank Thorwald, and George Williams.
 The film was released on September 19, 1920, by Paramount Pictures.
Copies of the film are in the Museum of Modern Art and at other film archives.
Square Deal Sanderson is a 1919 American silent western film directed by William S. Hart and Lambert Hillyer and written by Lambert Hillyer and Charles Alden Seltzer.
 The film stars William S. Hart, Ann Little, Frank Whitson, Lloyd Bacon, Edwin Wallock and Tom O'Brien.
 The film was released on June 15, 1919, by Paramount Pictures.
 A print of the film is held by the Library of Congress and in other film archives.
The Testing Block is a 1920 American silent Western film directed by Lambert Hillyer and written by Lambert Hillyer and William S. Hart.
 The film stars William S. Hart, Eva Novak, J. Gordon Russell, Florence Carpenter, Richard Headrick, and Ira McFadden.
 The film was released on December 26, 1920, by Paramount Pictures.
The Branded Sombrero is a 1928 American silent adventure film directed by Lambert Hillyer and written by Lambert Hillyer and James Kevin McGuinness.
 The film stars Buck Jones, Leila Hyams, Jack Baston, Stanton Heck, Francis Ford and Josephine Borio.
 The film was released on January 8, 1928, by Fox Film Corporation.