operating systems – Simultaneous buffer access in the bounded buffer problem

Galvin and various other resources only allow either the producer or the consumer to access the buffer at a time, the common code is as follows:

//Producer code

While(true)                     
{ down(empty);
  down(mutex);
  buffer(in) = item;
  in = (in+1) % buffer_size;
  up(mutex);
  up(full);
}

//Consumer code

While(true)
{ down(full);
  down(mutex);
  item = buffer(out);
  out = (out+1) % buffer_size;
  up(mutex);
  up(empty);
}

Here empty and full are semaphores which count the number of empty and full buffers. Mutex is initialised to 1, empty to buffer_size, full to 0.

I understand that multiple producers or consumers accessing the buffer at a time results in a race condition, but in my opinion a producer and a consumer can simultaneously access the buffer at a time without any problem. The solution given below seems to be fitting the constraints more precisely, so my question is, is there any problem(bounded wait not being satisfied, race condition, etc) in letting the producer and consumer access the buffer simultaneously like so?

While(true)
{ down(empty);
  down(producer_mutex);
  buffer(in) = item;
  in = (in+1) % buffer_size;
  up(producer_mutex);
  up(full);
}

While(true)
{ down(full);
  down(consumer_mutex);
  item = buffer(out);
  out = (out+1) % buffer_size;
  up(consumer_mutex);
  up(empty);
}