why it's a good idea to read widely -- so you're not overly influenced by one author
That is a very good (and important point). Those who won't read in the genre they have chosen once they start writing because they "they want to be original and don't want to be influenced" don't realize how excessively they will be influenced by whatever it is they have already read, or seen in a movie, or played in a role-playing game, that made them think they would like to write in that genre. Reading in the genre is important, so that you know what has already been done to death, and, hopefully receive some inspiration from what is good, to assimilate and combine with other influences. But a variety of reading outside the genre (and that includes non-fiction as well as fiction, can inspire fresh ideas by that same process of assimilation).
But I think this is also true:
That may very well be a good sign - that you are reading deliberately, and hearing the words in your head. That's exactly the kind of reading that will help your writing, rather than the breezy skimming that a lot of high-volume readers employ.
Because that kind of deliberate and thoughtful reading can be more helpful in assimilating ideas than just gulping down a story.
(Confession: I tend to be a gulper when I love a story. I can't wait to see what happens next. Zoom, I just go right through. But I do go back and reread the parts that impressed me, giving them closer attention.
And with writers who put together words beautifully, who I know produce striking images, I usually read more slowly in order to savor their work. I always do this, for instance, when I am reading books by Patricia McKillip or Tanith Lee.)