Well, she trust her "best friend" more than random girl. Beside she choose the bad one as her "best friend". That is where her fate took a bad turn. Or has it already begun?
TBF, Katrina still good before they announced who will be Prince fiancee. Rachel know Katrina before she plotting to throw her under the bus to take over her position.
Rachel basically like Anna, guileable and kind hearted person. had the position switch and Katrina is Anna close friends from child, it would cause the same outcome.
Rachel is raise by good family. she didn't exposed to scheming nobles and didn't expect that her "best friend" is the most venomous snake.
even in the main series she is shocked to learn how backstabbing Katrina is. that is after she experience all of it. at this timeline she is not yet learn about that. Also not help the Prince didn't tried to get close to Rachel as Rachel is have Noble upbringing and oblivious about common people struggle because she never being taught by her tutor not her parent.