The author states Occam’s Razor incorrectly from the get-go.

He says, “Occam’s Razor states that the simplest explanation for a problem is usually the most accurate.”

Actually, Occam’s Razor states that all things being equal the simplest explanation is preferable.

Originally, Occam’s Razor was used to distinguish between two hypotheses of equal predictive value. Otherwise, the simplest explanation would be preferred no matter how stupid the hypothesis is.

In common usage, Occam’s Razor is cited when trying to determine which hypothesis is most accurate. That’s using the original intent of Occam’s Razor backwards. It should only be used when there is a lot of data. Enough to at least to give a reasonable guess about the predictive value of the hypothesis. In common use, OR is cited when people don’t have much of an argument and resort to, well, “the simplest explanation is probably correct.” Yeah, all things being equal.

A better explanation is below (My emphasis.)

Occam’s Razor
One principle of note in regards to the scientific method is Occam’s Razor (alternately spelled Ockham’s Razor), which is named after the 14th century English logician and Franciscan friar William of Ockham. Occam did not create the concept - the work of Thomas Aquinas and even Aristotle referred to some form of it. The name was first attributed to him (to our knowledge) in the 1800s, indicating that he must have espoused the philosophy enough that his name became associated with it.

The Razor is often stated in Latin as:

entia non sunt multiplicanda praeter necessitatem

or, translated to English:

entities should not be multiplied beyond necessity

Occam’s Razor indicates that the most simple explanation that fits the available data is the one which is preferable. Assuming that two hypotheses are presented have equal predictive power, the one which makes the fewest assumptions and hypothetical entities takes precedence. This appeal to simplicity has been adopted by most of science, and is invoked in this popular quote by Albert Einstein:

Everything should be made as simple as possible, but not simpler.

It is significant to note that Occam’s Razor does not prove that the simpler hypothesis is, indeed, the true explanation of how nature behaves. Scientific principles should be as simple as possible, but that’s no proof that nature itself is simple.

However, it is generally the case that when a more complex system is at work there is some element of the evidence which doesn’t fit the simpler hypothesis, so Occam’s Razor is rarely wrong as it deals only with hypotheses of purely equal predictive power. The predictive power is more important than the simplicity.

And here are the first couple sentences from, oh horrors, Wikipedia, which agrees with the first link. Again, my emphasis:

Occam’s razor , is the meta-theoretical principle that “entities must not be multiplied beyond necessity” (entia non sunt multiplicanda praeter necessitatem) and the conclusion thereof, that the simplest solution is usually the correct one.

The principle is attributed to 14th-century English logician, theologian and Franciscan friar, William of Ockham. Occam’s razor may be alternatively phrased as pluralitas non est ponenda sine necessitate (“plurality should not be posited without necessity”). The principle is often expressed in Latin as the lex parsimoniae (translating to the law of parsimony, law of economy or law of succinctness). When competing hypotheses are equal in other respects, the principle recommends selection of the hypothesis that introduces the fewest assumptions and postulates the fewest entities while still sufficiently answering the question. It is in this sense that Occam’s razor is usually understood.