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1. I have a brother.
2. She said she had a brother. [ This is indirect speech.]
The above is wrong since her brother is still alive.
3. She said she has a brother. [This is the correct sentence.]
Your thoughts are welcome.
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2. I don't think someone can automatically make the assumption that the brother isn't alive any more from that context.

I think that's a good sentence. Remember, the English speakers highly prefer the past after past, NOT the present.
3. Also OK, more specific in pointing out that the brother is still alive.
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Thanks Marius
It seems you will approve both sentences.
In my book it would be incorrect to use 'she said she had a brother'.
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Let us take another example.
5. I love him.
6 She said she loved him.
It should be the following:
7. She said she loves him. [ If she is still in love with him, you should write this sentence.]
No, I don't think you get the feeling of English here:
She said is in the past.

She loved him is in the past.

Both are simultaneous. There's no conflict, we report it at the respective time frame.
Direct: I love him.
Reported at present tense: She says she loves him.
Reported in the past tense: She said she loved him.

She said in 1960 that she loved him then in 1960 [in the relative NOW of that time] , not that she loves him today in 2008. We do not care how she feels about him in 2008.
Thus I'm saying that:
She said she loves him.

is in effect much less correct.
At the BBC site:
0 from bbc.co.uk for "she said she loves him"
6 from bbc.co.uk for "she said she loved him"

At the New York Times site:
0 from nytimes.com for "she said she loves him"
7 from nytimes.com for "she said she loved him"
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On your original sentence:
At the New York Times:
0 from nytimes.com for "she said she has a brother"
http://www.google.com/search?hl=en&q=site%3Anytimes.com+%22she+said+she+has+a+brother%22&...
2 from nytimes.com for "she said she had a brother"
http://www.google.com/search?hl=en&q=site%3Anytimes.com+%22she+said+she+had+a+brother%22&...