There are certainly duties and operations which could, for one reason or another, require that the personnel involved not disclose the specifics of their work, possibly even decades later. I have worked with people who had previously worked on BMEWS, and because the specifics of some of the technology are still technically classified (despite being almost completely obsolete) they could not speak about the specifics of their work. Direct action operations–those involving timely or tactical work against a specific opponent–are generally less sensitive after a few years, but specifics of the operational methodology or tools may still warrant restricted access.
However, anybody essentially telling you, “I have a secret, but I can’t tell you what it is,” is just being at best boastful about a triviality, and more than likely is lying to you. And even elite operators have publicly accessible records of their service. Even US Army Special Forces operators, Navy SEALs, et cetera, all have to fit into the military bureaucracy, which includes records of service and promotion that are accessible by the general public. The actual duties may be hidden behind a false assignment or detachment, and medals and citations may be themselves classified, but no one who has ever been in the military has been told to answer “no” to a legal query about their status as current or former military in any normal (non-operational) context, and in fact failure to do so is in violation of the Uniform Code of Military Justice for an active or reserve duty soldier or officer. Anyone who was a true operator in a restricted group performing classified work is going to just give you an innocuous story, e.g. “I was a supply clerk in the 303rd Logistical Studies Group” and leave it at that.
BTW, even former operators with a legitimate background who go public about their identities and operations–like former SAS troop “Andy McNab” and 1SOFD-D operator Eric Haney–are regarded pretty dimly by former associates, especially when they capitalize on their former career by embellishing accomplishments for print or Hollywood. Some yokel who claims to be an ex-SEAL or former Force Recon, and is now working fast food or a clerical job? That’s smearing it on thick. Most retired operators go into private security or consulting, for which there are no lack of jobs.