Aren't you both saying the same thing?
Nope.
Think of flipping a coin: you can get a run of head, head, head, head, head relatively easily, so from a sample of five you could conclude that the coins are weighted to fall heads-up. But if you carry on flipping, you will get more tails and, if the coins are not weighted to fall one way preferentially, you will, fairly soon, have about half heads and half tails.
It's the same when you talk to people. Say you want to ask people's views on gay marriage. By fluke, your first ten people pounced on in the street might all be in favour and you start to think you've hit a very liberal town. But the more people you ask, the more representative your sample will be, and the less prone to chance. Talk to a couple of thousand of them, and you will have a very accurate view of what people in that town think - especially if you have carefully chosen your sample by age group, income, education etc to reflect the population of that town as a whole.
Consequently, it's the absolute size of the sample that matters, not the relative size compared to the population. Various people who can think in numbers and symbols have worked out the margin of error and the confidence level of various sample sizes. See here for info on margin of error. This sort of stuff is used all the time in audit, for example: it means auditors will only test a sample of transactions rather than redoing them all. And when people are enrolled in health studies - look at 10,000 smokers for ten years, and you'll get a very good idea of what goes wrong with their health. If you're a smoker, it won't tell what WILL happen to you, but it will let you judge how likely it is that something MIGHT happen to you.
I hope that's clear... As I said, I was crap at maths.