The graph in your first link is absolutely fascinating. I found the number of "Unintentional Poisoning" and "Suicide" deaths especially surprising (due to the high numbers)
Suicide means "the deceased ended their life, and had the intent to do so". The US says that people under the age of 9 cannot make a reasoned decision about killing themselves, and thus cannot have the intent to die.
So there will be some people under 9 who killed themselves. It will be a very small number. But their death will be counted as something other than suicide.
10 Leading Causes of Injury Deaths by Age Group HighlightingUnintentional Injury Deaths, United States – 2011
2007 - https://www.cdc.gov/injury/wisqars/pdf/unintentional_2007_bw...
2008 - https://www.cdc.gov/injury/wisqars/pdf/leading_causes_injury...
2009 - https://www.cdc.gov/injury/wisqars/pdf/leading_causes_injury...
2010 - https://www.cdc.gov/injury/wisqars/pdf/10lcid_unintentional_...
2011 - https://www.cdc.gov/injury/wisqars/pdf/leading_causes_of_inj...
All Data - https://www.cdc.gov/injury/wisqars/LeadingCauses.html