Against advice, when my infant son gets small bumps I often jump up to hold and comfort him while he bursts into tears. Is it true that I shouldn't react with this behaviour?

For young babies, I would think that it is alright to cuddle and comfort him when he had a fall. This is just to assure him that “mummy is there”. As he grows older, you can teach him how to react to such minor bumps. For example, to assess for himself how he is feeling (how bad did it hurt) and to go to you for washing of wounds and medication if needed. You will probably need to “let go” as well so that he can learn to handle such situations.