Do I mis-remember what those books said? Did geologists actually believe something like that? I guess those books must have been from the 1970s or earlier, but still.
Maybe its about defining what a news-worthy ice age means. It for sure shouldn't be just snowball Earth type when most of the planet apart from a bit of equatorial places froze solid white.
In any case, while we're currently in an "interglacial" period with respect to the Pleistocene glacial cycles, we're actually still in an "icehouse" period by the big-picture definition, since there are continental icesheets on Greenland and Antarctica. By contrast, a lot of the rest of the Phanerozoic has been characterized by "hothouse" climates, where there are no major continental icesheets anywhere on Earth.
It's possible that anthropogenic CO2 emissions will prevent us from going back into a colder "glacial" period when we otherwise next would have ~80 kyr from now, but geologic time is long and there is a lot of it still in front of us.