I am 'one of these people' - well, not in the way you describe - I'm certainly not a narcissist and I'm not a 'grief thief' but I do react in certain ways to other people's grief and emotions. I can see how it can be percieved as selfish and I can see how it can be misunderstood.
I have ADHD and one symptom/related behaviours of that are hypersensitivity. So for example, something like seeing somone cry makes me cry, and I find emotional films quite stressful. If someone shouts at me I find it really stressful and may cry or have a child-like response. I am super aware of other people's emotions, and if someone is in a bad mood it makes me extremely anxious and uncomfortable. Giving me the silent treatment is absolute torture. Because of this I tend to try and fix things and get involved in the cause of other peoples' emotions. I am/was often told I am ovrereacting or being ridiculous or oversensitive.
I also have rejection sensitivity. So if I've upset someone unintentionally, or someone criticises me, my knee-jerk reaction is absolute mortifying anxiety and an emotionally charged scramble to explain/fix it/undo it. My uncontrolled reation could be to cry, or to have a panic attack.
But I am also generally very empathatic and a people pleaser, which I have learnt from my Mum. Again, sometimes not helpful on both sides. But it brings me geniune and great joy to help people. Whether that is selfish or not is up for debate (altruism is an evolutionary trait that is ultimately selfish).
Believe me, I am very aware that my behaviour can be difficult for others. It can come across as selfish and it can be a coping mechanism that I adopt to protect myself from my emotions. It's really, really difficut for me and I wish I was different. It's led to depression an anxiety for my whole life and just coping with these extreme emotions is exhuasting. I try very hard and have been through a lot of therapy to help me override these knee-jerk reactions, and I am a much more balanced individual. As an analogy I would say that I am like someone who has arachnaphobia and is still absolutely terrified of spiders, but has taught themselves to be able to catch one and put it out the window instead of permanently avoid the room it's in!
So. I think lumping everyone into the same category and overgeneralising is really unhelful for both sides. People are wired differently and many people are neuroatypical to some degree. If someone comes across as 'selfishly empathetic' then there is probably a genuine reason for this and highly unlikely that they are actually a narcissist, which seems to be the Mumsnet go-to diagnosis.