Obviously you can't just apply for a new medical without an AME being involved, but it's more complicated than that.
I spent 12 years as a fed inside the beltway. It was not the FAA (so don't panic), but 5 years of that involved liaison work with other departments and I found a few things to be endemic in federal agencies. There are some exceptions, but most field offices are staffed with people with at least some, and sometimes substantial, specific program knowledge and subject matter expertise. However, in the central offices, and in administrative positions in central offices you start seeing an increasing percentage of staff with little or no program background or subject matter expertise. In fact, you start seeing an increasing percentage of people who have a law degree, but never practiced law, and may have never sat for or passed a bar exam. Universities churn out way more law school graduates than we need, and a large percentage of the surplus go into government thinking they are well suited to writing, implementing and enforcing regulations. They are not. In the absence of program knowledge and practical experience doing whatever that program/agency oversees, that legal trained person defaults to a narrow read of the law and that always ends badly from a practical, program focused perspective.
To you or I, if a opthamologist submitted a request to remove a restriction on a pilot's expired medical certificate, the logical response would be to contact the airman in question and advise them that the current medical is expired and that any request to remove a restriction would need to be done as part of an application for a new medical, then refer you to an AME to start the required application process. However, that's problematic for a couple reasons - there most likely isn't a category for such requests that is not connected to either a request for a new medical certificate or review of a current medical certificate. That's because the people who wrote the regs and sub regulatory guidance failed to either envision or account for this kind of request. Logically, an agency should be able to manage all sorts of very low probability/low frequency events like this one. As a practical matter however, they don't due to concerns about regulatory burden and the time and expense required to develop additional processes that are ultimately almost never used.
Given that background, a career bureaucrat with only a legal background will default to the legal requirements and a very narrow read of the law. In this case, that means it's an "application" to be approved or denied within a 60 day timeline. To that person, this request gets treated as an application because there is no other category to fit it into, or worse because it has already been put in the in-basket to process as an application by whoever opened it and stamped it in, with the result that it's already part of the performance monitoring process and the 60 day clock is already ticking. From that perspective, contacting the airman in question is all risk and downside with no upside. It takes time to contact the airman, and then the airman may take not take timely action or may take no action at all to continue the application process. If that action occurs slowly, or never occurs at all, the request (which is being treated as an application) will go over the allotted 60 day time limit and then be treated as a negative in both individual and agency performance metrics, as it was never approved or denied. The only control the staff processing it has is to treat it as an application and then deny it if no further information is received within the allotted time period.
Would that denial of a request on an expired medical mean anything to the airman? If would if it is counted and recorded as a denied application for a third class medical. If not, then it's not significant. The OP will need to consult with the FAA and with an aviation attorney to get an answer on that. Even then the answer from the FAA may still be "maybe" if they don't have some prior precedent and case law to work from. Feds cast in the legally trained the bureaucratic mold are generally speaking risk averse and their default response switch is safety wired in the least risk possible position.
That kind of mess gets created because the people who wrote the law, the regs and the sub regulatory guidance may not have been aware of or did not consider that this kind of thing could happen. Until the regs are re-written or sub regulatory guidance is written that creates a way to process this kind of misinformed request, it'll get treated as a new application, so it can be denied in a timely manner if no further action is taken. That inability to just ignore or return to sender an ill considered/misguided/inappropriate request is a negative and unintended outcome of laws requiring government accountability, internal controls, and performance requirements.
Unfortunately, not many federal employees are going to take the time or the risk to bump a request like this upstairs and make the argument that it is outside the scope of the law and should be treated as an exception. Trust me, advocating for that kind of realistic interpretation of law, reg, and guidance is not career enhancing, especially when the people up the chain of command are attorneys who know very little about the actual program and are much more concerned with performance measures based on timely adherence to process.
Then there is also the element of potential bureaucratic inertia. I don't know how the medical branch views Basic Med. They could see it as a big positive and a way to reduce workload, they could disagree with the whole idea see it as a threat to air safety or, particularly the folks higher up in the branch, they could see it as a threat to their kingdom by reducing the size, scope and authority of the branch. in either of the latter two cases, this request could be seen as an opportunity to dig into an airman's basic med cert and demonstrate that the process failed and that the airman operating under Basic Med, should not be flying.
In short, it's either being treated as an application in order to just deny the request (on what is an already expired certificate) get in the outbox within 60 days. Or alternatively, they are using it as a means to assess the quality of, or even disprove that Basic Med, as a concept, is working.