The concurrency bug in the provided code stems from the fact that multiple threads can access and modify the shared dictionaries (`self.jobs` and `self.results`) simultaneously without synchronization. Specifically:
1.  **Race Condition on Check-Then-Act:** Multiple threads can pass the `if job_id not in self.jobs` check, leading to the same job being processed multiple times.
2.  **Race Condition on Write:** Multiple threads can attempt to write to `self.results` or delete from `self.jobs` at the same time, causing data corruption or errors.

To fix this, we need to introduce a `threading.Lock` to protect critical sections. Furthermore, to allow high concurrency (so threads don't block each other while processing), we should remove the job from the `jobs` dictionary *before* processing begins (claiming it), and only hold the lock during the dictionary operations.

Here is the complete fixed implementation:

```python
import threading

class JobQueue:
    def __init__(self):
        self.jobs = {}
        self.results = {}
        # Initialize a lock to synchronize access to shared state
        self.lock = threading.Lock()

    def add_job(self, job_id, data):
        # Protect the write to the jobs dictionary
        with self.lock:
            self.jobs[job_id] = data
        return job_id

    def process_job(self, job_id, processor):
        # Acquire lock to safely inspect and modify the jobs dictionary
        with self.lock:
            if job_id not in self.jobs:
                return False
            
            # Atomically retrieve data and remove the job from the queue.
            # Removing it here (claiming it) prevents multiple threads from 
            # processing the same job_id simultaneously.
            data = self.jobs.pop(job_id)
        
        # Perform the actual processing outside the lock.
        # This allows other threads to add or process other jobs concurrently.
        result = processor(data)

        # Acquire lock again to safely store the result
        with self.lock:
            self.results[job_id] = result
        
        return True

    def get_result(self, job_id):
        # Protect the read from the results dictionary
        with self.lock:
            return self.results.get(job_id)
```

### Key Changes Explained:
1.  **`self.lock`**: Added a `threading.Lock` instance in `__init__`.
2.  **`add_job`**: Wrapped the dictionary assignment in a `with self.lock` block to prevent race conditions when adding jobs.
3.  **`process_job`**:
    *   **Atomic Claim**: Inside the lock, we check if the job exists and immediately remove it using `pop()`. This ensures that only one thread can "claim" a specific job ID to process.
    *   **Release Lock**: We release the lock *before* calling `processor(data)`. This is crucial for performance; otherwise, the queue would be serialized, and no other jobs could be added or processed while one job is running.
    *   **Safe Write**: We re-acquire the lock to write the result to `self.results`.
4.  **`get_result`**: Wrapped the dictionary access in a lock to ensure thread-safe reads.