They must have been using different crates for you (different region or perhaps era). For me they were standard plastic bins[1] with a separate “cold bag” inside for frozen stuff. No actual styrofoam I recall, although this was also over 10 years ago so I could be misremembering.

[1] https://www.uline.com/Product/Detail/S-9745G

The style of plastic bin definitely looks the same. The ones we were getting looked something like this[0], same folding-flap top as in your link but form-fitted insulation inside:

[0] https://flexcontainer.com/product/insulated-molded-container...