Assuming you wash your other produce (you probably should, especially if you buy organic and don't like e. coli.), the question you're asking is just "how does the crap on the outside get into the inside?" The usual route for those contaminants is peel -> hands -> fleshy fruity bits. A lot more is transferred than you might think.
For a bit of fun, try the same idea with a few dirty potatoes. Wash two thoroughly, and leave one unwashed. Peel a washed one, peel the unwashed one, and peel the last washed one. You'll observe that both of the latter two are much dirtier than the first one [0]. It won't be as dirty as what you started with, but it'll still be enough to cause some minor taste issues and (depending on the type of soil) make the dish feel gritty as you eat it. Contaminants you can't physically see/taste/feel are transferred the same way.
[0] There's a minor confounder in that potato flesh can oxidize, and that discoloration might be perceived as dirt. It's not as bad as with, e.g., apples though. Just work quickly, and the difference in dirt levels should be apparent.
For a bit of fun, try the same idea with a few dirty potatoes. Wash two thoroughly, and leave one unwashed. Peel a washed one, peel the unwashed one, and peel the last washed one. You'll observe that both of the latter two are much dirtier than the first one [0]. It won't be as dirty as what you started with, but it'll still be enough to cause some minor taste issues and (depending on the type of soil) make the dish feel gritty as you eat it. Contaminants you can't physically see/taste/feel are transferred the same way.
[0] There's a minor confounder in that potato flesh can oxidize, and that discoloration might be perceived as dirt. It's not as bad as with, e.g., apples though. Just work quickly, and the difference in dirt levels should be apparent.