Pretty much. And it's SOUL silver not shiny gold -_-......... You just get like a few different pokemon in each game. No biggy.
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Yes the same way you get shiny Pokemon in the other Pokemon games is how you get shiny Pokemon in heartgold. There is a free shiny Pokemon in the lake of rage.
I believe you can get a Shiny Stone in HeartGold in the Pokèathlon Prize Corner after you get 5000 Points.
The Shiny Stone does not exist in Pokemon Gold, Silver and Crystal it was added when Diamond and Pearl came out and if you're referring to Pokemon HeartGold, the Shiny Stone can be found at the National Park and can be won if you come in 1st place in the Bug Catching Contest.
You can buy the Shiny stone at the pokeatholon dome
To get any Shiny Pokemon, you need: LUCK