Please read 'A Prevalent Misconception About Sample Size, Statistical Significance, and Clinical Importance'
http://www.joponline.org/doi/abs/10.1902/jop.1972.43.3.181?j...
http://www.joponline.org/doi/abs/10.1902/jop.1972.43.3.181?j...
If the data source we tap is valid (i.e.: it does give us the information that we really need) then we need a big sample size to gain precision. If, otoh, the data is not valid in the first place then neither a small nor a big sample size are helpful.
It's a common misconception that the conclusions of a large study always are more trustworthy than from a small study. A larger study will however be able to detect smaller effects and will, as you mention, provide more precision.
What you seem to be referring to is whether or not a sample is representative of a population, which is indeed a critical factor in statistics, but not really related to the issue here.