Here is the corrected implementation of the `JobQueue` class that fixes the concurrency bug using proper thread synchronization:

```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]

        # Execute the processor outside the lock to avoid blocking other threads
        try:
            result = processor(data)
        except Exception:
            return False

        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 Choices:

1. **Thread Synchronization**: All accesses to shared state (`jobs` and `results` dictionaries) are protected by a `threading.Lock`.

2. **Lock Scope Optimization**:
   - The job is removed from `self.jobs` inside the lock to ensure it won't be processed again.
   - The `processor` is executed outside the lock to avoid blocking concurrent operations.
   - The result is stored back inside the lock to ensure thread-safe assignment.

3. **Exception Handling**: If the processor raises an exception, the job is not marked as completed, and the method returns `False` to indicate failure.

This implementation ensures correctness under concurrent access and prevents race conditions while maintaining good performance characteristics.