This certainly is the case! Translation is a creative process, not merely transformative, let alone mechanical. Especially with classics, where much interpretation is needed. The very first line of the Odyssey is a perfect example - the word used to describe Odysseus famously has no direct translation, so everyone puts their own spin on it.
Reading the amount of thought that goes into a translation is always interesting to me - for instance the introduction to a Sir Gawain and the Green Knight I have really helped me understand how the alliterative style worked and why the translation was done in a certain way (and why it was so hard).