Here's the fixed implementation of the `JobQueue` class that addresses the race condition using proper locking mechanisms:

```python
import threading

class JobQueue:
    def __init__(self):
        self.jobs = {}
        self.results = {}
        self.lock = threading.Lock()

    def add_job(self, job_id, data):
        with self.lock:
            self.jobs[job_id] = data
            return job_id

    def process_job(self, job_id, processor):
        # Atomically claim the job to prevent concurrent processing
        with self.lock:
            if job_id not in self.jobs:
                return False
            data = self.jobs.pop(job_id)  # Remove immediately to prevent reprocessing

        # Process the job outside the lock to allow concurrency
        result = processor(data)

        # Store the result under lock to ensure thread-safe write
        with self.lock:
            self.results[job_id] = result

        return True

    def get_result(self, job_id):
        with self.lock:
            return self.results.get(job_id)
```

### Key Fixes and Design Decisions

1. **Thread-Safe Access with Locking**:
   - All accesses to shared data (`self.jobs`, `self.results`) are protected by a `threading.Lock`, ensuring atomicity and preventing race conditions.

2. **Atomic Job Claiming**:
   - Using `pop(job_id)` inside the lock atomically removes the job from the queue, preventing multiple threads from processing the same job.

3. **Non-blocking Processing**:
   - The actual job processing (`processor(data)`) is performed outside the lock, allowing multiple threads to process different jobs concurrently and improving throughput.

4. **Safe Result Storage**:
   - After processing, results are stored within the lock to avoid concurrent writes to `self.results`.

This design ensures correctness under concurrent access while maintaining efficiency by minimizing lock contention.