Not really true. 700 is standard sample size. I hope there is a good dose of oversampling in these polls.
I am a scientist by trade with an MBA. I laugh at samples of 700-800 with multiple demographic factors as they have track records of being more inaccurate and I place them at the 85-90% confidence interval. That is + or - 10 to 15%. When data points hit 1000 they start to approach the 95% confidence interval. 1100-1300 fall more comfortably into the 95% interval and that is the minimum number I find that is valid before I accept any survey data as a fairly accurate cross section on data with multi-factors.