These days it is probably not possible to use your Pyrex Glass Double-Boiler on a glass smooth top range. Pyrex Glass Double-Boilers, and their related coffee pots, and tea pots were made for stove-top usage at a time when most stoves were gas stoves, which did not present a problem when low and medium flames were used. When electric coil stove usage grew, it was found that a defuser was needed to protect the cookware and to prevent breakage. The defuser lifts the cookware a bit off of the element so the heat is less direct, letting hot air heat the bottom and sides of the pot. I just checked my coffee pot and double-boiler set, and neither of them actually have very flat bottoms, something that is required for today's smooth-top ranges, but not required for most gas or electric coil ranges.
Corning was the maker of the first radiant glass-smooth top electric stoves in the early 1970's, and they supplied each stove with a set of their Corningware white-glass cookware for usage on those stoves. So it was not any ideas about "glass on glass cooking" - the stoves were calibrated for the cookware, and the cookware had polished smooth-bottoms. In any case in late 1980's, Corning sold its Housewares division - meaning it no longer makes any Pyrex or Corningware cookware - those famous pyroceram white dishes with the blue cornflower, or its stoves, etc. Corning became a company that focused on glass products like fiber optics, glass for computers, cell-phones and electronics, etc.
In any case another company, World Kitchen now makes the Pyrex-labeled and Corningware-labeled products, but they changed the formulas of the products so that they can only be used in the oven, not for the stove-top. For generations there was Pyrex BAKEWARE - the casseroles, the pie plates, mixing bowls, etc. that have the name PYREX embossed on the bottom of the dishes. From day one - these items were meant for the oven - where uniform heat surrounds the dish to cook the food. These items were never meant for the stove-top, but also happen to be what many people refer as "Pyrex" since the older doubler-boilers, coffee and tea-pots were no longer made. The formula for the Pyrex oven-ware was changed to a soda-lime type which works fine for oven-usage, and which is supposed to with-stand bumps and bruises. This soda-lime type has been used for decades by many folks without incident, and is marked clearly not for stove-top usage. Add in a few scare stories about "Pyrex exploding" via the internet and TV, and fear is generated.
So now floating around are two types of "Pyrex" and "Corningware" products - the older stuff that was clearly built and designed for the stove-top, and the older casseroles and pie-plates designed & built for the oven, as well as the newer types available in stores right now labeled "Pyrex and Corningware" that can only go in the oven. Add in the rise of glass smooth-top ranges where the makers can be sued if the instruction manuals say that a certain type of cookware can be used, and that cookware somehow "explodes". I believe that for liability reasons, because the stove makers could not always know just what kind of "Pyrex" or "Corningware" is being used on their stoves - in a blanket way state that no glass-cookware of any kind be used on their stove-tops.
Throw in glass smooth-top induction stoves which need magnetic pans - which leads to the idea that only suitable metal pans should only be used on any kind of stove top. Plus many of the current smooth-top electric stoves are calibrated for usage with metal pans, and not for the older pots that have not been produced for a long time. So the problem becomes one where if there is any damage to the smooth-top electric stove, or to the cookware - it would become the fault of the user, and the user would have pay for all repairs. So it becomes a "proceed at your own risk" type issue, where many just might opt to be safe, even if the product just might work.
All is not lost. One your Pyrex Double-Boiler is a great nostalgia piece from the days of Bewitched and the Brady Bunch. Many folks make their own "double-boiler" by using a metal pan for the bottom and a Pyrex bowl resting on top. Depending upon the size of the lower metal pan, you might be able to use one of the "pots" of the double=boiler set. In either case the bottom of the Pyrex bowl or inner pot should not touch the bottom of the pan of boiling water or actually "sit" in the boiling water, but rather rest above it, to get the low simmering that you need.
There are even ads for defuser type items for usage on smooth-top ranges. Many smooth-top ranges include a "simmer-burner" or keep-warm burner" for very low temperature tasks. I know that this message is long-winded, but I felt a better explanation and a little history was needed.
Mike