Your assumption (bolded) is incorrect. She was COVID positive sometime between Purim and Pesach. She tested positive for antibodies (Mt Sinai) with a result she was told was relatively a high number. When she tested more recently (probably late Sep) with this local doctor, he told her the number was a little over immunity level (ie implying that there had been a drop).
Okay, so here's a different assumption
When the doctor said "a little over immunity level" he probably meant "a little over antibody threshold level", that is, a little over the number that is used to conclude that the antibody test is positive. Nobody knows yet what level of antibody will provide the immunity needed to avoid a second infection.
Re Israel, what use is a positive/negative antibody result if it doesn't imply anything about current state of infection or potential immunity? I don't see how it's useful unless you assume some level of immunity.
Israel's goal is to decrease entry of virus into the country, balanced by the economic and social needs to allow travel. They're not at all interested in any individual's particular level of immunity, nor interested in how this will change over time. They just want to know, on that day that you're flying, what's the chance that you're bringing in live virus.
A positive antibody test implies that someone PROBABLY has been exposed to coronavirus, and PROBABLY is immune, and so is PROBABLY not carrying live virus now. There's a lot of uncertainty there, but based on our knowledge of other coronaviruses, let's say we're 95% certain they're not carrying the virus. So a group of antibody-positive travelers is much less likely to import the virus than a random group of people coming from NY/NJ. Some infected people probably WILL enter, but hopefully very few. If Israel is trying to ramp up travel, it makes sense to begin by allowing this group in first, and seeing how it goes. (Actually, they rescinded permission for this yesterday, I think, not sure why.)
But decisions we make for groups of people - public health - is not always the same as decisions made for individual health.
If 95% of Ab+ people are immune today (and I totally made up this number), it still means that 5% of Ab+ people are susceptible to infection/reinfection/transmitting the virus to others. And that 5% will increase over time as immunity weakens.
As an individual, my goal is to prevent illness to myself and others. The antibody test doesn't give a yes/no answer to immunity. If I'm Ab+, I wouldn't say "Now, I'm immune, I can spend time with my great grandmother." Rather, "Now there's a 95% chance I'm immune, and only a 5% chance that if I spend time with my great grandmother, I'll infect her and cause her death." We need to keep that (still unknown) probability in mind when we make our decisions.