In this old question, it is said that ただのNOUN and NOUNだけだ are used thus:
If you meant to say, "It's just an ordinary snake" or the like, it needs to be ただの蛇だ。 If you meant "It's only a snake", as in a case where you were expecting a Yeti, it would be 蛇だけだ。
However, in this article, the author says it's the other way around under the same circumstance:
Saying “It’s just a rock.”
I read the article on NihongoShark first last month, so I am quite annoyed now to see that people seem to disagree on something that I thought was meant to be a simple, and common usage. Personally, I find NihongoShark's detailed explanation and given context more convincing. However, since I once saw a few unnatural expressions on the website (can't remember what they were anymore), I have to take everything with a grain of salt.
Whose claim do you agree with?