What does "三年無改於父之道, 可謂孝矣" mean?

Today I was reading Edward Slingerland's book "Confucius Analects, with Selections from Traditional Commentaries" and came across the following translation of part of Passage 11 in Book 1 (1.11):

"If for three years he does not alter the ways of his father, he may be called a filial son."

In the commentary to the passage, the following was written:

Three years (usually understood as into the third year, or twenty five months) is the standard mourning period for a parent. As Kong Anguo explains, "When his father is still alive, the son is not able to act as he wants [because he must obey the father's command], so one can only observe his intentions in order to judge his character. It is only once his father has passed away that the son can learn about his character by observing his actions....

Even after reading the commentary, the translation of what Confucius supposedly said did not make much sense to me. What does "alter the ways of his father" mean, for example? Anyway, I looked up the original Chinese and found that Mr. Slingerland did, indeed, mistranslate the passage or, at least, fudge on some of the details. Here is the Chinese and my translation:

三(삼)年(년)無(무)改(개)於(어)父(부)之(지)道(도), 可(가)謂(위)孝(효)矣(의).  

Three (三) years (年) without (無) altering (改) duties to [one’s] father (於父之道) can (可) be called (謂) filial (孝), indeed (矣).

孝道 (효도) means "filial (孝) duties (道)" or "filial (孝) obligations (道)." According to Confucianism, a father and son have certain moral obligations or duties to each other. The father's obligations are called "父道 (부도)," which means "a father's (父) duties (道)," and a son's obligations are called "子道 (자도)," which means "a son's (子) duties (道)."

The above passage was referring to a son's "filial (孝) duties (道)" to his father, which included performing all the required rituals for mourning his father for three years after his father's death. Mr. Slingerland mistranslated "於父之道 (어부지도)" as "from the ways of the father." Instead, he should have translated it as "duties to [one's] father," with the 於 (어) meaning "to," and 道 (도) meaning "duties." In other words, the son would be altering his "to-father duties." But why didn't Confucius write 孝道 (효도) instead of just 道 (도)? Because Confucius wanted to save the filial (孝) description of 道 (도) for the climax of the sentence, which was, "[such duty] can (可) be called (謂) 'filial (孝),' indeed (矣)." In other words, Confucius indirectly and, I think, cleverly formed the word "孝道 (효도) with his sentence.

By the way, "altering one's filial duties to one's father" could include skipping certain time-consuming or expensive mourning rituals.