Unless you had a contract stating otherwise, you were an at-will employee and, as such, subject to termination at any time, regardless of whether the reason is fair or true. Thus, termination under the circumstances you describe would not violate any law.
Your entitlement to unemployment benefits has nothing to do with the legality of your termination. The EDD's only concern is whether you were fired for "misconduct" as defined in the applicable regulations. So, it's entirely possible that your benefits may be granted but you don't have a case for wrongful termination. Indeed, based on the facts you have provided, that would seem to be precisely what has happened.
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You really have no case to bring, let alone a strong case of winning. Unless you have an express agreement to the contrary, you are an at will employee. That means you can be terminated for any reason or even no reason at all as long as it is not for an unlawful reason. An employer of an at will employee is allowed to terminate an employee based on erroneous information if it so desires. The fact that the drug report came back as positive for marijuana is more than sufficient basis, even if there are questions that you could raise about the accuracy of the testing.
You ask about unemployment benefits. Rather than point to it as proof that you engaged in no misconduct, I would be thanking my lucky stars that the employer did not contest the award. Testing positive for drugs is considered "misconduct" and would otherwise disqualify you from benefits. However it the employer did not contest the EDD determination to give you benefits, you apparently have otherwise qualified.
Good luck to you.
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I agree with both of my colleagues. Unfortunately, based on the information you provided, the employer has not done anything illegal that would give rise to a claim. However, if you are a member of a union or have an employment contract, you may have a potential remedy.
It's not clear from your question what "case" you are referring to, but if you mean a lawsuit for wrongful termination then no. You were most likely an "at will" employee. This means you could be terminated for any reason, or no reason at all, at any time so long as it isn't based on discriminatory reasons (i.e. because of race, sex, national origin or another protected classification), or your having engaged in a protected activity, or in violation of the terms of a contract or collective bargaining agreement. Being “at will” also means that the employer is not required to justify the decision with “good cause.” On that basis your termination would not have been unlawful, and you would not have recourse notwithstanding that you are receiving unemployment benefits.
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Unless your employer expressly or impliedly promised that you would only be terminated for cause, you do not have a claim for wrongful termination. However, you may have a claim for defamation. If your employer told you that you were fired because you were on drugs and hit someone, and if you are forced to repeat the reason for your termination to other prospective employers, then you may be able to sue for defamation under the "compelled self-publication" doctrine. Obviously, a defamation claim can only be brought if you can prove that the employer's statements are false.