This is, to my knowledge, a true statement.

The NP with Scimitar came along in 1904, the "NITRO PROOF" came along in 1896. ("NITRO PROOF" mostly seen on shotguns?)

That said, after 1896 and up to 1904 not all rifles were marked this way. There are rifles in my collection from that time frame that are marked with the appropriate Cordite charge and bullet weight (Express Rifles) but are not marked "NITRO PROOF".
I think that prior to 1896 Proof was Proof and calibres such as the .303 British (1891) were just assumed to be in proof with period ammunition.

Having said that, "if" the rifle or gun in question is not marked either with the proof marks or Cordite charge and bullet weight then it cannot be assumed to be proved for or with Cordite or other smokeless powder.

Interestingly enough, when Cordite (Modite/Rifleite/etc) appeared on the scene in 1889, and the Cordite .303 British Mk1 loading in 1891, the Proof Houses for some time continued to use Black Powder for proof loads. They simply adjusted powder and bullet weight to achieve the increased pressure of smokeless.
- Mike