"Infant death syndrome kills most babies that share beds with parents"? Wrong. Misleading. That would mean that out of 1,000 babies who share beds with their parents, more than 500 die of SIDS! This is not true.
Out of 100,000 babies, roughly 15000 share beds with their parents [see note 1 below], and 97 (per 100,000) die of SIDS or SIDS-related causes (hereinafter "SIDS"). 
What this article implies is not that there are more than 7500 SIDS deaths out of those 15000 bed-sharing babies(!), but that, of the 97 deaths (per 100,000 babies) from SIDS, about 71  were in bed-sharing babies and about 26  in babies who did not share a bed with their parents.
In other words, for babies who sleep on their own, the SIDS death rate is roughly 1 SIDS death per every 3300 babies , and for babies who sleep with their parents, the SIDS death rate is roughly 1 SIDS death out of every 210 babies .
According to the available data then, by having a baby sleep with its parents, its risk of death from SIDS does not just double, triple, or quadruple—it increases to about 15 times the risk of death from SIDS for babies who sleep on their own. 
Even at that the risk is still "small." Statistically, in a town of 10,000 bed-sharing babies, only about 47 will die of SIDS. But in a town of 10,000 babies sleeping on their own, only 3 will die of SIDS.
So it is wildly inaccurate to say "[SIDS] kills most [of] the babies [who] share beds with parents." I think most people would have noticed by now if over half the bed-sharing babies were dying!!!
It is, however, accurate to say "Most babies who die of [SIDS] share beds with parents," if you are describing a study (this one) that says that of every 3 SIDS deaths, 2 are in babies who share beds with their parents. 
The take home message, though, is that bed-sharing babies are about 15 times as likely to die from SIDS as are babies who sleep alone.
 A study found a rate of 14% in 2010, and that rate had increased from 7% in 1993, with bed sharing continuing to increase in popularity. http://www.cnn.com/2013/10/02/health/bed-sharing-infants-increases/
 SIDS/SUIDS, accidental strangulation/suffocation in bed, or unknown/undetermined cause, at rates of 55 per 100,000; 27 per 100,000; and 16 per 100,000 babies, respectively: http://mchb.hrsa.gov/chusa13/perinatal-health-status-indicators/p/SIDS-SUID.html; I chose 2009 data for the purposes of this analysis, as they were closest to the data used in the Pediatrics study: http://pediatrics.aappublications.org/content/early/2014/07/09/peds.2014-0401.full.pdf+html.
 69.2 percent of 97 = 71.34
 97 - 71 = 26
 26/85,000 = 0.00030588 = 0.03%; 1/0.00030588 = 85,000/26 = 3269
 71/15,000 = 0.004733333333 = 0.473%; 1/0.004733333333 = 15,000/71 = 211
 3269/211 = 15.49
 69.2%. Be careful not to misinterpret this statistic! The fact that only 15 percent of babies are bed sharing, versus 85 percent that are not, means that, given the overall SIDS death rate of 97 deaths per 100,000 babies, bed-sharing babies die from SIDS at a rate that is 15.5 times the rate of SIDS deaths for babies who do not share beds, as explained above. If you are reading this as bed-sharing babies having only twice the rate of SIDS death, you are either assuming that just as many babies are sharing a bed as are not [a bed-sharing to non-bed-sharing ratio of 50/50, rather than 15/85] or you may need to brush up on math.