I think that's wrong. They should be able to provision a new service using a second port on your ONT, instantly. At least, I've seen people who've done other ISP-to-ISP migrations like that, by taking new service from another ISP and then either keeping or cancelling the old service.
Probably the person you're talking to has no idea what an ONT is, let alone a 4-port one.
Of course, the proportion of FTTP services with 4-port ONT is going to get smaller and smaller over time, so less-well trained staff will become less likely to come across them.