You were probably suspended to give the employer time to prepare your last paycheck. This is a fairly common practice, especially when payroll is processed by a third-party payroll service. If you were fired on the spot, the employer would have been required to pay you immediately.
Unless you have an employment contract or are covered by a collective bargaining agreement, there is no such thing as a "legitimate reason" to let you go. As an at-will employee, you can terminate your employment at any time, and so can your employer.
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In California an employer can fire an employee for any reason (except unlawful reasons like race or age discrimination or harassment, etc.). So yes, it was lawful for the employer to terminate your employment citing safety issues. The employer didn't have to cite any reason.
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I agree with my colleagues. In California, the general rule is that an employer can terminate an at-will employee for any reason, no reason. Even if the reason the employer gives the employee is an obvious lie (which happens a lot). What an employer cannot do is terminate you for reasons related to your membership in a "protected class," meaning race, religion, ethnicity, national origin, sexual orientation, gender, etc. Nor can an employer terminate you for a "protected activity" such as asserting a right to be paid overtime or for being a whistle blower. Thus, your termination based on safety issues, even if completely false, is legal.