This is hopefully beyond obvious, but if upper management ever says something like this, it is time to at minimum start working on making other opportunities available to you.
Whether you do this by interviewing, networking, blogging, public speaking, or whatever your preference is doesn't matter much. As long as you do something.
In my personal experience, whenever anything like this happened, there would be layoffs within a year. Also whenever management would make an official statement addressing "rumors", saying that "everything is fine, zero risk of layoffs", layoffs happened within a year.