grammaticality - Is using "she" when the gender is unknown ungrammatical?

I often come across the use of "she" not as an gender neutral pronoun as such but as the pronoun of choice when the gender is unknown. This is particularly common in scientific/technical documents but not exclusive to them. The following are four of the first google hits when searching for "the user can" "if she":

• Example 1:

  
  
  

  
  

  The user can type anything to identify the file. When coming back to the data she would expect to see exactly the same string she typed in.

  
  




• Example 2:

  
  
  
  

  
  

  In this page the user can add a new entity, if she follows the link labelled Add entity.

  
  




• Example 3:

  
  
  

  
  

  To continue with our ergonomic program, imagine that you would really like the user to sit down and your program would continue only once she answers that she is sitting down, you can use the do…while statement to wait for the user to sit down;

  
  




• Example 4:

  
  
  
  

  
  

  The user can program the alarm to go off at a particular time -- for example, the user can enter the time when she expects to get home.

  
  

I do not call this gender-neutral because she clearly has a gender. However, that is in no way implied by the context. Traditionally, we would have used he instead but the use of she in these contexts has been rising (at least that is my impression).

I raised this point in the comments section of this question and was told that such use of she is ungrammatical. I was also told that it is annoying which is the reader's prerogative, but ungrammatical?

So, is such use of she ungrammatical and, if so, why?

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CLARIFICATION: I am not asking what the gender-neutral pronoun is in the English language but why she would be ungrammatical if he isn't.