The author lives in Ireland. Hence he's most likely a native speaker.

Is it just me or do others also have the impression that it's mostly native speakers doing this incorrectly? Or are there some schools/conventions/… where "it's" is correct or at least an acceptable alternative?

In my experience, native speakers make a distinctly different class of mistakes from non-native speakers. Non-native speakers almost always learn the language formally in some sort of class, with a book and a curriculum. The mistakes tend to be simple memory failures, or incorrect analogies with their native languages. For example, a French-speaking person might say "rape the cheese" because "rape" is how you say "grate" in French, and they've forgotten that it's a false friend. Chinese speakers will say "he" instead of "she" a lot (or vice versa), because spoken Chinese doesn't distinguish and they're not used to tracking the sex of the subject. (Both totally real examples I've seen.)

Non-native speakers, on the other hand, learn the language informally, and they learn it spoken long before they learn it written. Really formal education in the language doesn't start until they're generally fluent. Thus you get mistakes like its/it's and your/you're and their/there/they're. Native speakers grew up with these as single words (it's all based on sound, after all!) and only later had to learn to distinguish them. Non-native speakers, on the other hand, were exposed to them as separate words from the start, and so don't typically mix them up.

Very good point. I had never done mistakes like these before moving to the US, and at the time English was not my primary language. A few years later, I make these mistakes more and more often.

I tend to blame this on the fact that, at the beginning, speech was less natural than writing (I was writing scientific articles before moving to the US) and I made several non-native-speaker mistakes (rape/grate and he/she) in writing. Now I am making fewer of these but increasingly more of the "it's/its" type, possibly due to speech becoming more of a natural act and therefore driving my writing. Because "it's" and "its" sound the same, I might overlook it in writing too. "Should of" and "should have" seem to fit in this case as well.

[Edit: last sentence]

My personal theory is that native speakers are so used to those words being similar that they don't care about the difference so much. For people who learned English later on it's/its are two completely different words. At least that's how I see it. I see native speakers confusing them much more often than foreigners I know. There's a similar issue with even more crazy mistakes... I've never seen a foreigner write "should of" ('ve) - but many people in Bristol do that all the time.

I live in Ireland, we dont really get taught a whole lot of grammar in school, or else I had terrible terrible teachers.

Answer: No, no one considers it correct, and if they do, they shouldn't!

I would like to mention that it always seems a bit dickish when someone bothers commenting saying 'hurr durr there's supposed to be an apostrophe here', no one knows if the author has dyslexia, or if he is in fact a native speaker (Legally, our native language isn't English btw, most people are only English speakers, but there is a tiny minority who aren't).

/rant

I don't understand why people get upset about these corrections. If I make a mistake, I'd rather be told than not. If the person making the correction is a jerk, sure, that's no good, but that wasn't the case here and usually isn't.

And many, many more grammatical errors in the article itself.