Can Apple hack into its own iPhones at will?

It's doable via a hardware hack.

The iPhone 5 does not have an SE (Secure Enclave), which means that the persistent store for the 10 count is in the flash itself.

So as long as you are willing to reset the flash to its previous state after every 4 attempts, it's doable from outside iOS.

To do it would require a reflow oven, a lab, a microscopic soldering station, and a BGA chip socket for the flash part itself.

If you wanted to do it faster, you'd need a BGA socket for the flash part that that let you run a cable into it, and, without electrical interference from the iPhone circuitry itself, reset the flash part to its original (current) state after every 4 attempts.

Basically, if the count never goes past 4, there's no delay, and if the count is reset before reaching 10 times, it never gets to the point of wiping the contents.

Of course...

The FBI doesn't want a hardware hack, because they already know that they could do this themselves, pay Apple to do it, or send it off to ChipWorks in Canada, and have it done for them.  They want a proof of concept software hack.

At which point it's likely that they will demand that this be made a feature of iOS itself, so that they can read out any iPhone.

In other words, they want a software "Clipper Chip" for iPhones.