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Hager inadvertently sent a email critical of the work ethic of three players to the entire squad following a defeat during the recent World Cup.
Since the incident, some players have spoken out about a negative environment in the Black Sticks.
Earlier this week Hockey New Zealand confirmed it will conduct an independent review into the team culture.
Glynn, who made 134 appearance for the Black Sticks between 2009 and 2015, has joined with a group of former internationals, which includes Krystal Forgesson and Emily Gaddum (nee Naylor), in refuting claims he created a negative environment.
The 29-year-old said high performance sport was tough, and that Hager challenged his athletes but never mistreated or bullied players as alleged.
''Mark is a person of high integrity and has always created a high-pressure training environment designed to challenge players physically and mentally,'' she wrote in an open letter.
''Mark never allows the group to become complacent and he always has every player in the squad pushing and challenging for selection.
''Through Mark's high expectations and low tolerance of complacency, this became ingrained in us as individuals and we were constantly striving for better performances and demanding more of ourselves in both trainings and in games - this essentially led us to being successful, strong and resilient as a group.
''We always had a positive and supportive team environment amongst players and our coaching staff. We did not feel bullied, mistreated, or that Mark was playing mind games with us.''
The Black Sticks finished a disappointing 11th at the World Cup, three months after winning gold at the Commonwealth Games.
''Since taking over the team [in] 2009, Mark has achieved many outstanding results with this group and many firsts for New Zealand Hockey as well as taking the team from 13th to 3rd in the world in our prime.
''He still today continues to achieve results no other coach or New Zealand Women's Hockey team has done before.
''We all respect Mark, and we always had a challenging but positive experience playing in this group and look back fondly on the great memories we have.''