Wild onions are hard to kill by organic means because the bulbs can persist underground for years. There are herbicides that kill wild onions. Here is a link to a fact sheet from Clemson University called "Wild Garlic and Wild Onions".
Can I use any of the recommended products in flower and shrub beds? The article you attached addresses wild onions in lawns.
It depends on what it says on the label of the herbicide. By law, herbicides will have specific information about where you can use them and what to avoid. One way I avoid harming nearby plants is to paint the herbicide directly onto the target plant. I would bend and bruise the foliage and then carefully paint the leaf surface. If the onions are close to other plants, you can use cardboard to shield them. I've also used a gallon plastic jug with the bottom cut off and the top hole made larger. I set the jug over the weed and paint the weed through the top hole. That way I know nothing is getting carried in the wind to other plants.