You're confusing criminal and civil, "innocent until proven guilty" is criminal and you left out the most important part "beyond a reasonable doubt".
Civil cases are not a question of guilt or innocence, they are a question of liability.
Because both US and Canadian law all derives from British law the procedure is the same. The only differences is in the terminology used (ie: preponderance of the evidence in the US, Canada its balance of probabilities).
Read this for a better understanding of how both systems work.
Canada
Code:
http://www.justice.gc.ca/eng/csj-sjc/just/08.html
US
Code:
http://www.uscourts.gov/aboutfederal-courts/types-cases/civil-cases