Welcome to the forum.  Be prepared to be overwhelmed with information about your Carbine.  I fear you may end up being more confused than when you came in.

The short answer is "no".  All carbines do not have saddle bars and rings.  But here is where the confusion will begin.  Your Carbine is furnished with a  "short" stock rather than the longer, replacement stock that was issued for updating many carbines after 1899.  That, longer, stock had no ring or bar.  But, according to Col. Brophy who wrote "The Krag Rifle Story", in fiscal year 1901, 736 short, original length, stocks were produced without the provision for the bar and ring.  He has no indication of a reason for their manufacture.  And here is where your Carbine gets really interesting - at least to me.  I have seen, including yours, 4 of these short stocks, fitted with the 1896 Carbine rear sight, the high barrel band with sight protectors, and short, original length upper hand guard.  In addition, all three were are in exceptional condition, and most interestingly, all 3 have the receiver marked with only the date of 1896 without the word "Model" in front.  That particular detail is the rarest of the variety of marks on the Krag.  In addition, all were within the expected serial number range for such a receiver marking.  But there is still a puzzle with your Carbine.  That lies with the cartouche. None of the other examples had a cartouche.  All had the Circle "P" like yours and an initial between the "P" and the trigger guard.  And, if your stock was made in fiscal 1901 there would be no reason to have a date of 1896.  All other details are those of a especially nice 1896 Carbine.  At least two of the carbines were made with the shorter stock produced in Italian Walnut (appropriate for a 1900 -1901 date) while the hand guards appear to have been the original Black Walnut - probably correct given the rarity of the use of these guards at that time.  Your father should, indeed, be thrilled.  You did good.