Cathy,
I think I owe you a large apology. Some of the birth dates for Alfred's siblings are decidedly odd, and furthermore there is no birth registration for an Alfred Smith with the mother's maiden name Dennis within 100 miles of Derby in 1919.
If we start from William Henry Smith's marriage to Margaret Dennis in 1907 at St Luke's in Derby, they appear to have had several older children who had left home by the time of the 1939 Register; there's Reginald William born (?16 March) 1909 who died in 1981; then there's William H born 1913, followed by Margaret A born 1915 who appears to have died two years later.
There is then a gap until Alfred's birth is registered in Qtr 1 1917, (not 1919). There is then a birth of Arthur Smith, mother's maiden name Dennis in Derby during the last quarter of 1919. We then get another anomaly. In the 1939 register brother Albert's date of birth is shown as 20 Oct 1924, yet his birth is registered in quarter 4 of 1923. Antony's entry in the 1939R and his birth registration agree. The last entry in the 1939R is for Eric whose birth date is given as 16 Oct 1932 (when mother Margaret would have been in her 43rd year) but his birth was registered in the last quarter of 1931.
Given the fact that Alfred's, Albert's and Eric's birth dates are so muddled, I think it is highly likely that
Alfred though born in 1917 was actually brought up with his parents thinking he was born in 1919, perhaps confusing him with Arthur. If that is the case then the newspaper may have got the details about Alfred's age from his parents, not an official source, further adding to the confusion.
If all of that turns out to be a reasonable explanation, then the newspaper article at least provides one additional piece of information about Alfred, namely that he was in the Royal Army Ordnance Corps, and worked in a mobile bath unit. I think the fact that two of his brothers are also mentioned by name in the article is too much of a coincidence for this not to be the right man.
