Almost all intransitive verbs take が (e.g. ドアが開く、電気が消える)
→ These "が" mean that the words before them such as "ドア" and "電気" are subjects of the sentences. Not only intransitive verbs but also transitive verbs DO take this kind of "が" like "私がドアを開ける(私が~開ける)" and "私が電気を消す(私が~消す)". So, this is not a problem of whether it is intransitive or not. (It is not correct here to put it in the same category as that of "を" he is asking about.)
....but there are some exceptions - intransitive verbs that don't take が. And 休む is one of those (仕事を休む、会社を休む)
→ From the viewpoint above, it is obvious that even these "exceptions" DO take "が" like "彼が仕事を休む(彼が~休む)" and "彼女が会社を休む(彼女が~休む)とは驚いた".
入る is another example of an intransitive verb that doesn't take が (it takes に): お風呂に入る
→ This example also DOES take "が" like "患者がお風呂に入る(患者が~入る)時は介護士が助ける".
→ As I have pointed out above, it is not appropriate to explain these three particles "が", "を", and "に" in the same category as she did. Other than that, I have to say what she wrote here is not answering his question at all.
【His question】
Why can we use the を particle with 休む in Japanese if it is an intransitive verb?
such as
仕事を休む to take off time from work
→ Exactly. With some intransitive verbs that mean movement from one place to another, you sometimes use this kind of "を". It means the starting point of your action just as you said "from" in your English phrase "to take off time from work" or a place where you do the action. /e.g. 故郷を離れる。大学を去る。荒野を行く。道路を走る。etc. / Just to let you know, with some other intransitive verbs that mean the opposite, I mean "come to one place from another", you sometimes use "に". I suppose this "に" is not so difficult as that "を" above because it naturally means almost the same as English prepositions such as "to", "into", and "for" do. /e.g. 高校に入る。屋敷に忍び込む。東京に向かう。etc.