I'm recently back from a break from PRO, and found that when I beat Birch in my Hoenn boss cycle, he happened to be a third-time victory. After choosing a Treecko, I was delighted to be offered a choice to either sync it or try for a shiny one. Since I hadn't brought a sync, I chose the shiny chance. With this in mind, I went through the process of training up my timid sync to level 100, so I could try for a Sigilyph from Suhuzen.
However, after beating her (which was harder since I had to open with a Xatu) I wasn't given any such option. My brother tells me that all the bosses he's tried recently gave him the aforementioned choice, so I would like to know if this was a bug, or if there is a list of bosses with/without this feature. If so, could someone please share it?
P.S.: If someone could tell me what the shiny chance is for situations like this or the game corner, I would be very grateful. I think I've seen the number 1/500 thrown around, but can't be sure.