That's the question.
What qualities should be looked in a bedding for an infant to prevent the crib deaths?
Does sealing the bedding with a strong polythene sheet provide any benefits or risks?
These recommendations are those repeated by many reputable health care and pediatric groups, and are commonly recognized as the standard best-practices in modern pediatrics.
This is the recommendation associated with a rather controversial, and disputed, theory. Starting with Barry Richardson's 1989 "Richardson Hypothesis", and later continued by Dr. Jim Sprott, the hypothesis theorizes that certain fungi can break down some specific chemicals present in some children's bedding material, and convert it to "toxic 'nerve' gasses". The suggested solution to this is to wrap the mattress in special materials to prevent this "toxic nerve gas" from reaching the baby.
Dr. Sprott continues to support this theory, however, and claims it to be scientific "fact", rather than a theory (in my personal opinion, this is one of the big danger signs warning of quackery: no scientific theory is ever proven as "fact", and stating a minority opinion as "fact" is quite telling, imo). This is based upon his campaign to wrap mattresses in New Zealand, and an overall decrease in "cot death" fatalities (again, a correlation of this nature is far too weak an argument to declare a theory as confirmed, imo).
Here is a discussion about the theory that brings up some good points. Mainly that Dr. Sprott directly profits from this theory, since he apparently markets both his own line of "approved" mattress covers as the "cure to SIDS", and also his own book on the subject.
On Dr. Sprott's website, he makes quite clear that only his product is safe (the FAQ mentions several times that other covers are not safe, citing repeatedly his "Cot Life 2000" protocol, which apparently states that all types of materials must be enclosed in his patented cover; note that I can find no evidence that the government of New Zealand in any way endorses this "protocol").
Under no circumstances do I think any parent should undertake to wrap their child's mattress in their own polythene sheet; it seems even Dr. Sprott does not feel this is safe to do as a "DIY" project.
In my opinion, "sealing the bedding with a strong polythene sheet" presents a significant risk of suffocation -- not SIDS, just plain asphyxiation. Most infant mattresses are deliberately covered with a mesh webbing underneath the cotton surface with the explicit purpose of allowing the baby to breathe even if it turns face-down during sleep.
Try it for yourself: bury your face in your own pillow and try to breathe. It's neither easy nor comfortable, but you survive. Now wrap a plastic bag around your pillow and repeat -- you'll notice that it's completely impossible to breathe!
For this simple reason, any and all material in and near an infant's bed must be a "breathable" type. Baby pillows, bedsheets and teddy bears present a suffocation danger simply because they might end up in front of the baby's face during the night.
Frankly, the text in the source originally stated in your question is scary, but really the scary thing is that some human being wrote that text and seems to believe that baby mattresses really contain "highly toxic nerve gases." Why would there be phosphorus or even arsenic in a mattress? Such stupidity! Please please never believe such panic-mongering. You were right to doubt that text. I'm glad you posted your question!
all the guidance we got suggests that putting plastic wrapping anywhere near a mattress is a very bad idea. Like Chrys says, you do not get 'nerve gases' from mattresses, and in fact letting air get through a mattress is a much better idea.
Babies should not have a pillow, but should be laid on the mattress, with one breathable blanket under them.
This breathability allows them to breathe if they do roll onto their front. It also allows spittle, milk and vomit to move away from baby's mouth!