A PM has to compete with all the other PMs to get her features implemented. And if the PM's feature gets implemented first, this PM looks super productive.
I think if you're an product manager looking to be the best product manager, taking credit is imperative. Because at the end of the day, your feature is just paper until it is implemented.
Not being hated, well, that's another matter... I sympathize with the enormous friction between folks who assign work and folks who finish it.