I think that if one were to go with the strict definition of the word "carve" - meaning "to make something by cutting into especially wood or stone, or to cut into the surface of stone, wood" - then it is fine. However, as I mentioned before, "carve" can have an association with art within a common psyche, i.e. carving a statue, or carving a wooded totem pole, and so when when using "carve" within the context of an archaeological artefact, especially when used in popular media for the general public, it can implant the idea into the mind that what was found was artistic or decorative, and not something utilitarian.
Certainly when I had read the head lines and articles I had thought of some carved artistic, shamanistic or totemic object. Indeed, before I had found the Historical England site, any images of the wood I seen were not actually showing "intentional cuts" and so I was left looking for the carved image, perhaps some rudimentary anthropomorphic thing. Indeed, I thought that I could make out a face, which the skeptic in me (rightly) dismissed as pareidolia as I could not discern how anyone could see it as being deliberately made.
So that is why, personally, I think using the more prosaic "intentional cut marks" phrasing is better than saying carved.
The real, and interesting question of course is what was the intention of the cut marks, and are they actually decorative, symbolic or utilitarian?
Jonny
The path to good scholarship is paved with imagined patterns. - David M Raup