How can a given project have SPI lower than 1 and still be on schedule? According to PMBOK, SPI>1 means ahead of schedule, SPI=1 means on schedule, and SPI<1 means behind schedule. But I was looking on some projects on the Internet and they were indeed on schedule, but their SPI was lower than 1. How is that possible? I'm a PM Student, not profissional yet.

It is not possible. Folks are reporting on time and ignoring the metrics because they can't cope with bad news.

Thinking about this a little more, I'd like to add this:

SPI, as with the other EV indices, are as the name suggests: indicators. As with all predictors, EV has predictive validity issues, i.e., nothing is 100% perfect. So while an SPI can show under performance, there may be other indicators that suggest better performance and, putting them all together, you would draw your conclusion of where you are in your schedule. You also have to remember that SPI is a lagging indicator. That plays into your analysis.

Nevertheless, if I had an SPI that was less than zero, I'd be hard pressed to conclude that I am on time except if I lost confidence in the EV reporting. But that would also mean that I am flying blind with all the risks therein.