It's true and untrue depending on how you look at it. Flash memory only supports changing/"writing" bits in one direction, generally from 1 to 0. Erase, as a separate operation, clears entire sectors back to 1, but is more costly than a write. (Erase block size depends on the technology but we're talking MB on modern flash AFAIK, stuff from 2010 already had 128kB.)

So, the drives do indeed never "overwrite" data - they mark the block as unused (either when the OS uses TRIM, or when it writes new data [for which it picks an empty block elsewhere]), and put it in a queue to be erased whenever there's time (and energy and heat budget) to do so.

Understanding this is also quite important because it can have performance implications, particularly on consumer/low-end devices. Those don't have a whole lot of spare space to work with, so if the entire device is "in use", write performance can take a serious hit when it becomes limited by erase speed.

[Add.: reference for block sizes: https://www.micron.com/support/~/media/74C3F8B1250D4935898DB... - note the PDF creation date on that is 2002(!) and it compares 16kB against 128kB size.]