Shiny pokemon are a very rare occurrence, that can indeed show up at any time in the game. You can even run into two shiny pokemon in a row, but the chance are slim, 1 in 8192 to be exact, which gives us a percentage of 0.0001220703125. It's kind of like the lotto for pokemon.
Now, as for the people with boxes of shiny pokemon; they use AR codes to make the appearance of shiny pokemon 100%.