At a dog seminar I asked the same question because I had heard so many conflicting reports.
The veterinarian that I asked was in his 90s. He told me it was an excellent question and said that unless a dog had a bleeding disorder, nipping a nail too short would only cause some bleeding. It is a good idea to have “quick stop” or another brand of “stop bleed” to treat the nail that has been clipped too short. If you don’t have anything else you can even use flour to stop the bleeding.
White nails are easier than black nails because you can see the vein.
Consistent nipping will help the vein to recede farther back allowing you to be able to nip more each time. I recommend nipping a puppy’s nails every week as it will help the puppy become more tolerant of this necessary action.