If it's a total write-off, then yes, it means the value is zero. But you can also write off a less-than-total loss. For example if my stock drops from $10 to $5, I can write off $5 in losses (assuming I sell at the lower value). In that example it didn't drop to zero.

So it depends if they're talking about a total write-off, or a write-off.

I think the misunderstanding comes from the fact that in everyday parlance, "write-off" often means a complete 100% loss (for example, my car was totaled, and it's a write-off). But in accounting, it does not.