Here we are trying to teach you that één means 1 and not a, which is een. Sure, using 'a' when talking may not be an issue, but it does convey a difference in meaning.
- a and een are indefinite articles.
- one and één indicate a number
Anyway, I personally think that the audio is clear enough: één is pronounced differently from een.
When accepting 'I have a brother' we are throwing away the purpose of this sentence(!), which is to teach you this difference, so I ask you to accept that we're looking for "I have one brother' as the answer instead. :)
It's part of standardized Dutch. Both een and één are valid to refer to the number with, but one must remember that een is also the indefinite article. This can quickly cause somebody to misinterpret the number as the indefinite article, as the indefinite article is such a common word. So, to disambiguate between the two, I personally determine if I should use één using the following criteria:
- I'm talking about the number one
- Een would also be valid when interpreted as an indefinite article
I've provided some more information below about the reason and logic behind the accents.
A bit more information
Acute accents (´) can be placed on the first two letters of a syllable to mark stress or emphasis:
- Dit duurt ééuwig! — This is taking forever!
- Weet je het héél zeker? — Are you really sure?
- Een uitstékende oplossing! — An excellent solution!
- Dat lied is écht ongelofelijk. — That song is truly incredible.
- Dat lied is echt óngelofelijk. — That song is truly incredible.
This is important in this case, because the article een is almost always reduced to something more like un¹ in spoken Dutch, whereas the number één is never reduced. Because of this, turning een into één will force the reader to read it in its full (unreduced) form, a pronunciation which nowadays is almost used exclusively for the number.
- Ik heb een broer. — I have a brother.
- Ik heb één broer. — I have one brother.
Leaving them out
Knowing this, it makes sense that the accents are not always necessary. If from the context een can only mean the number, somebody will likely already read it as één:
- Een van de mensen was te laat. — One of the people was too late.
People will understand you just fine in this example. I feel like this is the reason you were told you don't need them.
¹ Technically this particular sound is called a schwa and is different from an u—common in a lot of unstressed syllables with an e, such as most verbs. Happens in many English accents as well, e.g. the a in about.