Fred Brown wrote quite a wide variety of types of story, so such an an assumption isn't all that far wrong... but it is a bit inaccurate. Much of his sf, for instance, has a humorous or gallows-humor bent, while others are fairly straightforward and quite grim ("Arena", for instance). He also wrote mysteries, many of which are apparently quite good (I've not read them myself, but I've known plent of people who have, and whose opinions I would trust).
He also wrote a certain amount of horror or horror-fantasy, some of which might almost be called Lovecraftian, in a sense. "Come and Go Mad" is somewhat of that type and was, if I recall correctly, originally published in Weird Tales.
The connection to Bradbury I have a bit more trouble with, save that each used the sf tropes for their metaphoric value, in order to address this or that aspect of the human condition; but the approach is otherwise quite different....
Still, Brown is well worth investigating....