That's an interesting statement but you provide no substantiation for such a claim.
Perlite is made from Obsidian, a volcanic glass which is silica, the same silica found in playsand only it's amorphous while playsand has a hexagonal crystal structure the same as quartz. Silica is the second most common mineral after carbon. Obsidian is heated under controlled conditions until it expands into Perlite. There is a naturally occuring form of perlite found within some deposits of Obsidian that is called "Snowflake" Obsidian. Associated minerals that may be found within Obsidian are the Soda Silicates (feldspars) which create the "sheen" Obsidians often used in gemcutting, Tourmaline an aluminum silicate and Quartz. These associated minerals form within the Obsidian when super heated gases are infused into the volcanic glass while cooling. These gases slow the cooling process which allows the minerals to form in their more normal crystal structures. Interestingly Obsidian (amorphous), Opal (spherical) and Quartz (assymetrically hexagonal) are identical in their chemical makeup when in their pure forms.
Vermiculite is made from the Mica group, most commonly from Muscovite Mica which is a basic potassium aluminum silicate. It is found in three layer structures with Potassium, Calcium or Sodium found between the layers. Vermiculite is also made using a similar process to perlite which causes it to expand. If you look closely at your Vermiculite you can see the layers clearly. It was often used in the "olden" days as a substitute for glass as the layers could be flaked off thin enough to allow light penetration although it was/is translucent not transparent. The Mica group are metamorphic minerals found most often within Granite deposits.
(The above are summerizations taken from: "The Audobon Guide to Gems and Minerals", "Gemstones and Minerals Data Book", "Gemstones and Minerals for the Jeweler and Gemcutter".)
BTW the plastic that most of use in the form of shoe boxes for egg containers has been shown to be cancerous when heated in a microwave oven.
I would be interested to see any references you have pertaining to Perlite being cancerous. I'm not be a wisea$$ as you can see I have more than a passing interest in minerology as I'm a gemcutter and I am capable of learning new things.
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Hope this helps.
BigT