Here's the corrected and thread-safe implementation of the `JobQueue` class, with proper locking to prevent race conditions:

```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):
        with self.lock:
            if job_id not in self.jobs:
                return False
            data = self.jobs[job_id]
            del self.jobs[job_id]

        # Process outside the lock to avoid blocking other operations
        result = processor(data)

        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 Safety with Locking:**
   - A `threading.Lock` ensures that only one thread accesses or modifies shared state (`self.jobs`, `self.results`) at a time.
   - All dictionary operations that read or write shared data are protected by the lock.

2. **Atomic Job Removal:**
   - The job is removed from `self.jobs` inside the lock, preventing other threads from re-queuing or re-processing the same job.

3. **Processing Outside the Lock:**
   - The `processor(data)` call is performed outside the lock to avoid blocking other threads while the job is being processed. This improves concurrency and responsiveness.

4. **Consistent Result Storage:**
   - After processing, the result is stored under the lock to ensure `self.results` is updated safely and atomically.

This implementation prevents race conditions such as:
- Multiple threads processing the same job
- Lost or overwritten results
- Inconsistent state during job deletion and result storage

It balances correctness with performance by minimizing the time the lock is held.