Rifling on the SMLE Mark IV (Converted), which was th ONLY Mrk IV built, was identical to the rifling of the SMLE Mark III/III*, so he has to mean the NUMBER 4 Rifle.
ALL SMLE rifling was to the same pattern: bore bored, reamed and polished to .301 - .303, then rifled with an Enfield Cutter Box in increments of .0005", 5 grooves, left-hand, 1 turn in 10 inches, 40 passes for each and every barrel with inspections between pass series. The only exceptions were 2000 exprimental tapr-bore barrels (1000 each in 1906 and 1907, survivors removed and destroyed in 1924) and a series of experiments with pitches between 6 and 12 inches, 2 of each of which 1 was destroyed following the test. One of each remained in the Pattern Room when I was there in 1976.
Rifling of the NUMBER 4 Rifle was varied in the extreme. Ideally, the standard was the same as for the SMLE, but a small event called World War Two interfered with the plans. As a result, we have Number 4 barrels with 2, 3, 4, 5 and 6 grooves, right-hand and left-hand twists and anything else you can think of. Early Savage barrels and late Long Branch barrels can have 6 grooves, but they are different, the Savage barrels having regular Savage commercial-type rifling, the Long Branch barrels being broach-cut on Bren Gun machinery from John Inglis. MILLIONS of Number 4 Rifles were made with TWO-groove barrels, 3-groove was tried and failed, some were built with 4 (which I have never seen personally).... but the ideal remained 5. Fortunately, pitch was retained at 10 inches.
True Enfield rifling is quite unique, having lands and grooves of equal width. It is the perfected form of the modern 5R rifling...... except that it was used from 1896 onwards and never had a US Patent on it. It was designed by Sir William Metford. As well, the grooves are sharp-edged and comparatively deep.
If I were to encounter a NUMBER 4 barrel with what appears to be shallow rifling, I would think immediately of a very-early-production Savage 6-groove barrel, in which case it would be normal.
Otherwise, very shallow rifling usually means a burned-out barrel and will show much more emphatically at the breech end.
Hope this helps.