Details are often critical in legal issues. Please refrain from making things up.
Your wife has not received a speeding fine, or any other fine for that matter. She has received a Notice of Intended Prosecution which included a requirement under s. 172 Road Traffic Act 1988 to provide information regarding the driver's identity.
Ownership is largely irrelevant. The "person keeping the vehicle" has a more onerous responsibility than "any other person".
The former must name the driver, but has a defence if they provided any information that was in their power to give and that might lead to the identification of the driver and is able to satisfy the court (on the balance of probabilities) that they both do not know who was driving, and could not with reasonable diligence ascertain who was driving.
The latter is merely required to provide any information that is in their power to give and that might lead to the identification of the driver.
Whether/when a person is or is not the "person keeping the vehicle" is not well defined in law, but if she provided all the information that was in power to give, and could not with reasonable diligence ascertain who was driving, she would have had a defence either way.
From what little you have told us, she has not mentioned the mechanic who had control of the vehicle at the material time, nor explained why she does not know who was driving, and so would appear to be guilty of the s. 172 offence, assuming that the 28 days has expired. It sounds like the police are giving her a second chance to comply with her obligations, but from the lack of detail or accuracy of your account so far, it is difficult to be certain of anything.