How does the automatic property synthesize in xcode 4.4 work?

I'm new to Objective-C and XCode, but I was happy to see that XCode 4.4 automatically synthesizes my properties for me, now. I figure this means that I no longer have to type out @synthesize for my properties, and that I get to access them using self.propertyName = @"hi";, for example.

I'm trying to re-write some example code so that I can understand it better, but this code implements a custom getter method. In the example code, the property is manually synthesized, as @synthesize managedObjectContext = __managedObjectContext;. The custom getter looks like this:

- (NSManagedObjectContext *)managedObjectContext {
    if (__managedObjectContext != nil) {
        return __managedObjectContext;
    }
    
    NSPersistentStoreCoordinator *coordinator = [self persistentStoreCoordinator];
    if (coordinator != nil) {
        __managedObjectContext = [[NSManagedObjectContext alloc] initWithConcurrencyType:NSMainQueueConcurrencyType];
        [__managedObjectContext setPersistentStoreCoordinator:coordinator];
    }
    
    return __managedObjectContext;
}

In this person's code, I see he's just using his manually synthesized accessor to both get and set. I figured in my code, I could just replace the __managedObjectContext with self.managedObjectContext, but nope. If I do this, I get an error telling me that I am trying to assign to a readonly property. This makes sense, because that property is defined as readonly, by this other coder.

@property (readonly, strong, nonatomic) NSManagedObjectContext *managedObjectContext;

So, I figure something about how he's manually synthesizing his property means that if he uses that specified setter, it allows him to set a readonly property somehow.

If I manually synthesize the property, like in the code I am referencing, everything goes back to working, but that's not making use of the new automatic synthesize. If I remove the readonly, I can set this property, as expected, but I feel like I'm not understanding why he has it as readonly, so I bet I'm breaking something there.

So, am I misusing the new automatic synthesize? How do I set this using the setter, if the automatic synthesize is not creating it for me, because of readonly?