This summary is not the rule. The rule text controls.
When someone needs to prove that a subpoena or other court paper was properly delivered, they have to follow the same rules used in regular civil court cases (found in CPLR 306 and 4532). This means filling out the correct paperwork showing when, how, and to whom the document was given.
There's one important exception. If the person being served is under 16 years old, or if they are legally considered incompetent, they cannot simply sign a paper saying they accepted service. That kind of written admission doesn't count for them. Anyone who is 16 or older, and doesn't have a legal incompetence issue, can sign a written statement admitting they received the papers, and that signed statement will be accepted as valid proof.
This rule matters because it protects young people and vulnerable adults from being treated as properly served just because they signed something. Courts want real proof that these individuals actually understood and received the legal papers, not just a signature that might not reflect true awareness of what was happening.