[Sample size note: For all we know, 8 people texted in and only one of them (12.5%) said "no" but given the size of YES's audience, we'll assume that it's north of 100, making it relatively stable for analysis]
Pretty astonishing, right? The results bear no relation to reality whatsoever. Just look at how many people were still at the Mets vs. Cardinals game on Saturday night in the 19th inning compared to how many were there in the first:
You can't see the whole stadium, but it's probably safe to assume that the upper deck was even more sparsely populated given that people tend to move down to better seats as others leave. Saying that a quarter of the fans were still there would be fairly generous. And that game took place on a Saturday night, so it wasn't like most people had to get up for work in the morning.
So why is the poll so egregiously wrong?
First off, the sample is biased because it depends on people to volunteer to pick up their phone and take part in it. It's called participation bias. A text poll is always going to suffer from this type of error (as do online surveys, to a lesser degree), but if you wanted to get a better answer and still use a survey method, randomly asking people in the stands (and not at home) would give you more accurate results.
Furthermore, the average age of text polls are always going to skew younger and young people are the the ones who are more likely to actually stay for the game. Your grandfather probably isn't going to pick up his Droid and dial 58772 and there's a good chance that's he's gone long before the second seventh inning stretch rolls around.
Also, it's more likely that someone would text in to say "yes" as opposed to "no" since affirmative and/or positive answers are better at coaxing people to take part. Saying that you would leave early from an exciting game isn't something people are keen on admitting to because they think it makes them look like less of a fan. Surveys attract people by allowing them a chance to offer their opinion, so when they are somewhat ashamed or embarrassed by it, they are less likely to go out of their way to give it.
Most importantly, though, the question deals with stated intent, something that surveys often can't measure effectively. In a vacuum, I'm sure that people would like to stay and see all 20 innings of a game. It sounds great in your mind ("What an epic game!", "I'd never leave in the middle of it") but in actuality, there are a ton of small inconveniences that you don't bother to take into consideration.
It becomes uncomfortable to sit in the same crappy plastic seats for over 7 hours, especially when they stopped serving beer in the middle of the 7th and most (or all) of the other concessions stands are probably shut down as well. Of course people are going to claim that they would stick it out when they are sitting on their cushy couch watching the third inning of a game on a lazy Sunday afternoon, but when they are at the park, stomach growling, legs falling asleep, and eyelids seemingly increasing in weight, it's easy to turn to the person next to you and say "Do you wanna get the hell out of here or what?". Staying for an entire marathon extra inning game is a classic example of something that's "easier said than done" and surveys can only measure the "said" part.
So perhaps the headline was a little misleading. It's not that people are exactly lying; most aren't willfully misrepresenting their positions. This is just an example of a time when a survey question has no correlation with reality. I don't know if it's a bad question, necessarily, because no one is basing any decisions on the outcome of it, but the results certainly don't reflect the truth in any way shape or form.