You're welcome, Alliea, glad it helped! It's an old method, I learned from my grandfather (a farmer and nursery grower), then my mother. Never knew why it worked, just knew it did. Once I studied horticultural chemistry, the reason became clear:
Epsom salts adds important depleted trace minerals to the soil, as noted in the posts you found. In addition, it helps remove salt buildup in stems, that can come from certain minerals in soil, or commercial fertilizers and chemicals. This allows the stems to more readily take up moisture and nutrients from the soil. It's a more natural way of helping your plants get the right nutrition, without dumping commercial fertilizers and supplements on them.
Epsom salts are beneficial to thick or woody stemmed plants, and acid loving plants (they require trace minerals not often easily available or absorbed). Use it on hydrangeas, azaleas, rhododendrons, etc -- also veggies such as tomatoes and peppers. The plants will thrive, you'll see richer green foliage and vibrant flower color. Tomatoes and peppers will be full of good moisture and crisp flavor.
I use it on the lawns also, to help them green up in spring.
Some prefer to mix with water and spray on foliage. I'm a lazy gardener ... I just sprinkle it on the soil around the root ends (avoid getting it on the base of stems) and let the rain water it in 
btw, I love your rose and it's pretty reflection in the water! Happy gardening!
Those who contemplate the beauty of the earth find reserves of strength that will endure as long as life lasts.
~ Rachel Carson