There is a private method _setFocusRingType:
that appears to match the NSView API. I was able to use that to eliminate the focus ring, though this may not pass app review.
Use this at your own risk:
SEL selector = NSSelectorFromString(@"_setFocusRingType:");
NSMethodSignature *signature = [self.textView methodSignatureForSelector:selector];
NSInvocation *invocation = [NSInvocation invocationWithMethodSignature:signature];
[invocation setSelector:selector];
NSUInteger arg = 1; // NSFocusRingTypeNone
[invocation setArgument:&arg atIndex:2];
[invocation invokeWithTarget:self.textView];
Hopefully we get a real solution from Apple.