This is a fairly complex procedural question, but let's give it a shot. A demurrer is a challenge to the legal sufficiency of a pleading. For instance, for a charge of grand theft, the amount in question has to be over $950.00. If the complaint does not allege an amount over $950.00, it is subject to be dismissal by demurrer. If the defense does not demur, the complaint will proceed, but the prosecution must still prove the facts at trial. If they fail to prove the facts, the verdict will be not guilty. PC 1385 allows the court to dismiss a case on its own motion or that of the prosecution in the interests of justice. This grants broad discretion to the judge. "Interests of justice" equates to fundamental fairness. It does not include grounds for a demurrer as set forth above. It might include other factors such as the age or disability of the defendant. I hope this is of some assistance. Let me know if you have further questions.
I for one agree with you that the language you quoted is weird in this context. Usually 1385's are granted at the request of the DA cannot prove their case. If they charge you with grand theft in my colleague's example and the amount is $50 the complaint if demurrable, also subject to a PC 991 motion, and subject to dismissal under 1385.
Not to worry the dismissal gets you off the hook anyway.