My understanding is that since 9/11 the answer is no. SQ is correct about that. I have never understood why someone sending another person off at the airport would want to go to the gate anyway.

There is another thread here where the proposal is that you buy a fully refundable ticket using a credit card to a nearby location (so the ticket is not too expensive) at the airport, get a boarding pass then go through security, go to the airline desk and cancel the ticket (and get a refund on your credit card). Messy but can be done where there you can get purchase tickets from machines which will also issue you with boarding passes. Mainly US airlines and mainly domestic flights.

The problem is that SQ uses T4 at JFK where there is unlikely to be a US airline where you can follow the above process. I suppose the cash outlay and subsequent refund will have to be for a large amount. Given this is an international terminal, you also have to clear US immigration when returning landside; i.e. you need to bring your passport with you. Now that is going to take a bit of explaining as to why you are airside but did not fly into the country. Most of the discussions in the above thread involves domestic terminals and flights so US immigration is not an issue.

Not sure why you feel you have to accompany someone to the gate. For children or elderly passengers, there is likely to be a service where for a fee, you can get airport/airline staff to accompany the person to the plane.