No, cats can poo outside too. Cats are outside animals, you know. You're doing something wrong if you're letting it out of the house to explore the neighbourhood and then it comes back inside to stuff.
Litter Trays for cats should pretty much only be used if you have kittens, sick cats, old cats or live in a place without a garden/access to outside (like an apartment).
we mostly keep our cats inside or watch them while they're outside.
the older cat we let out into the garden in the front yard in the mornings and he just lays down under the bushes for a while. sometimes we'll let him into the backyard because it's all fenced off, but he never roams because he's too timid.
the younger cat is too outgoing to let outside unsupervised (we don't want our cats running loose because there are people in the neighborhood who shoot animals with pellet guns), but sometimes we'll let him into the enclosed garden in the backyard and he's pretty happy there.
neither of the cats use the bathroom outside though, they have litter boxes inside to use.