Now that you say the Body Text is a built-in text, I do feel like maybe what I did, aka deleting that style, is simply asking word to hide it. I mainly use the style gallery (the one in the tool bar) to see the styles but a doc should have more styles than that.

What I saw was that the copying and pasting into my template will add the Body Text style into the gallery. I deleted the Body Text from source doc before copying and that solved this behaviour. So yeah probably that's simply hidden, which is fine, as long as it doesn't change my template styles.

I compared the styles in source doc and template and Body Text was found in both files, but deleting Body Text style was allowed in source doc, so I guess after pasting into the template, the template's Body Text style just took over.