For me - and despite my username, I have no military experience; I am just a well-read student of BritishEmpire and its arms with plenty still to learn - the key thing in differentiating a parts gun from a refurbished arm is "who replaced the parts, why, and when?"
It goes without saying (at least in my opinion) that parts replaced by military or police armourers during the arm's service life do not compromise the historic integrity of the gun - and often adds to it, as for example with a Martini-Henry which was later converted to a Martini-Enfield.
But, if significant parts were replaced with "new" bits (even "correct" new bits) after a gun left service, then it's a different kettle of fish (with exceptions for trivial things like screws and sling swivels etc)
As an example: I would not classify a full-wood SMLE with only a post-service replacement barrel (even a New Old Stock or brand new one) as a "parts gun". Ditto a restored sporterised SMLE which has retained its original barrel but has "new" woodwork.
But an SMLE which has a post-service replacement barrel AND a replacement stock? I'd probably consider that a "parts gun", since at that point pretty much the only "original" parts left in it are the action and the magazine and it has no history behind it anymore.
It's still an SMLE, of course - replacing the barrel and the woodwork doesn't change that - but just as if you have a restored Model T Ford where the only "original" parts left in it are the steering wheel, the windscreen, and the dashboard; then I would suggest you're going to have a hard time convinving anyone it's an historic car - even if it's been completely and lovingly restored with care and patience to almost the same condition it rolled out of the factory in.
Having said all that, I believe the easiest way to establish a "good faith" restoration/refurbishment is to keep the parts that were on the gun when it was originally acquired. Even if it's a sporterised SMLE and the furniture and barrel and sight have been changed back to "original" ones, by retaining the "incorrect" parts the restorer ensures that whoever acquires the rifle after them is under no illusions of its earlier condition and how it has been altered.
I should also stress that I don't see anything wrong with taking a sporterised/broken/bitser rifle and refurbishing it to "as-new(ish)" condition so it can be used for target shooting or hunting; to the contrary I might even call that a noble and worthy undertaking.
But I believe the critical thing is that the restorer be open about what's been done, and that it's been done to recreate/restore a vintage rifle for modern, practical use - rather than passing it off as a rare Rhodesian Commando Marksman's Rifle which belonged to the grandfather of a friend of a friend who fought in the Mau Mau uprising.