I wish they gave a source for the relationship between using these pronouns and telling the truth.

The explanation is given in the paper, citing another study. Thankfully it's not paywalled (hooray for open access!) As the HN article is a summary of the academic paper [1], it probably omitted the detail for brevity.

Here's what the paper says:

  "The honesty of the status updates written by the participants was assessed
   following the approach introduced by Newman, Pennebaker, Berry, and Richards
   (2003) using LIWC. Their analyses showed that liars use fewer first-person
   pronouns (e.g., I, me), fewer third-person pronouns (e.g., she, their), fewer
   exclusive words (e.g., but, exclude), more motion verbs (e.g., arrive, go),
   and more negative words (e.g., worried, fearful; Newman, Pennebaker, Berry, &
   Richards, 2003)."

[1] http://journals.sagepub.com/doi/full/10.1177/194855061668105...

w/r/t selection bias, "As of the third quarter of 2016, Facebook had 1.79 billion monthly active users." https://www.statista.com/statistics/264810/number-of-monthly...

Their sample pool covers better than 25% of the human population.

While that's a very large pool, it's almost certainly not random.

What sample size or methodology for the question at hand would satisfy you at this point?

https://en.wikipedia.org/wiki/On_Exactitude_in_Science

A huge sample size does not necessarily mean a good sample. While it's difficult to say what the impact of sampling only from a group of people who self-select into a given population, it's clearly a bias. If a quarter of the population self-selects into Facebook, I'd prefer a sample that includes three times as many people who didn't.

If nothing else, it's worth considering the demographics: within the USA, women use Facebook at a higher rate than men; people with some college education use Facebook at a higher rate than either college graduates or adults who've never been to college; Facebook use rate is roughly negatively correlated with income level; use of Facebook is negatively correlated with age (http://www.pewinternet.org/2016/11/11/social-media-update-20...). So the leftover US population skews male and slightly higher-income than the Facebook population. And globally, Facebook use is correlated with national wealth (minus some outliers). So there's clearly a sampling bias, and that's worth understanding.

That said, whether the results would be any different is hard (impossible?) to say without actually trying a different sampling methodology, and I suspect the results from this study are valid, sampling bias notwithstanding.

A few hundred randomly selected people would give more certainty than billions that aren't randomly selected.