Your conception is entirely correct
: Except for a current recession rate of around 3.8 cm per year, the Moon’s orbit around Earth remains essentially stable elliptical with minor and major radii of 356,500 km and 406,700 km, respectively. Thus, any claims about the Moon being closer than ever before are demonstrably bunk. In fact, if the accepted collision theory of lunar formation is correct, the Moon was significantly closer to Earth many millions of years ago.
ETA: There is some variation in apogee and, more especially, perigee distances month-to-month due to the Sun’s gravitational action and the Earth-Moon system’s elliptical orbit around the Sun. When the system is at or near perihelion, the variation in perigee is greater because the Sun’s gravitational gradient is steeper the closer to it you are. In practical terms, while the annual perigee extremes can vary by about 1,700 km, the annual perigee minima vary by only a few tens of kilometres year-on-year. Strictly speaking, then, it’s accurate to say that in 2016 the Moon was closer to Earth than it has been since 1948, but the perigee variation from years prior to 2016 is hardly significant.