If a subclass refers to a superclass ivar, synthesizing an unrelated property fails

Edit: I just noticed this other Stack Overflow question asking much the same thing: Why does a subclass @property with no corresponding ivar hide superclass ivars?

This is some interesting behavior that I cannot find documented in anything official or unofficial (blog, tweet, SO question, etc). I have boiled it down to its essence and tested this in a fresh Xcode project, but I can't explain it.

MyBaseClass has an instance variable:

@interface MyBaseClass : NSObject {
    NSObject *fooInstanceVar;
}
@end

MySubclass extends MyBaseClass, and declares a totally unrelated property (that is, the property is not intended to be backed by the instance variable):

#import "MyBaseClass.h"
@interface MySubclass : MyBaseClass { }
@property (nonatomic, retain) NSObject *barProperty;
@end

If the implementation of MySubclass does not synthesize the property but implements the accessor methods, everything is fine (no compiler error):

#import "MySubclass.h"
@implementation MySubclass

- (NSObject*)barProperty {
    return [[NSObject alloc] init]; // pls ignore flagrant violation of memory rules.
}

- (void)setBarProperty:(NSObject *)obj { /* no-op */ }

- (void)doSomethingWithProperty {
    NSArray *array = [NSArray arrayWithObjects:self.barProperty, fooInstanceVar, nil];
    NSLog(@"%@", array);
}
@end

But if I remove the property accessor methods and replace them with a synthesize declaration for the property, I get a compiler error: 'fooInstanceVar' undeclared (first use in this function).

#import "MySubclass.h"
@implementation MySubclass
@synthesize barProperty;

- (void)doSomethingWithProperty {
    NSArray *array = [NSArray arrayWithObjects:self.barProperty, fooInstanceVar, nil];
    NSLog(@"%@", array);
}
@end

This error goes away if I remove either the synthesize declaration, or if I do not refer to the fooInstanceVar instance variable from within MySubclass.m, or if I put all interface and implementation definitions in a single file. This error also seems to happen in both GCC 4.2 and GCC/LLVM build settings.

Can anyone explain what's happening here?