Rules as Intended: Yes
Because to use Bodyguard, you must use an Attack of Opportunity against your foe. Although the whip does say you cannot threaten adjacent foes:
The whip is treated as a melee weapon with 15-foot reach, though you don't threaten the area into which you can make an attack.
The requeriment of Aid Another is simply that you are in position to make a melee attack against that foe:
If you're in position to make a melee attack on an opponent that is engaging a friend in melee combat
Meaning that you can use Aid Another even if you have weapons that normally do not threaten adjacent squares, such as Unarmed (without improved unarmed strike) or the Whip.
We can see this type of build supported on this thread, and also on this build. And also seems to be the intent of the Author of the feat:
Bodyguard is intended to require you only to be adjacent to the ally you're defending, not to require you to threaten their attacker. Requiring you to threaten the attacker makes the feat MUCH less useful, since then you can't block ranged attacks or reach weapons or attacks against targets with concealment or cover or anything else that would prevent an AoO. My intention with tying it to the AoO mechanic was simply to make it an ability you could use more than once per round, rather than wanting to tie it specifically to all the implied mechanics of AoOs. I had thought about just making it an immediate action, but that limits it to once per round and takes your im/swift action. I figured that was an appropriate mechanic for In Harm's Way, but the defensive bonus of AA was modest enough that I thought it entirely fair to not limit it that way.
As an side, I should say that for both feats, as well as the shield feats and shield-based archetypes I wrote, I thought that defender characters needed a little extra love in the rules, whether evil emperor bodyguards or altruistic protectors.
It's possible I had misremembered the mechanic for Aid Another, thinking that AA to add an attack bonus required an attack roll vs. AC 10 against the target while AA to add to AC required an attack roll vs. AC 10 against the defender. I can't really say for sure about my thought process 3 years ago, but that could have been the root of the problem.
But is not the official ruling as has been answered on this FAQ.
Note that you also will need Whip Mastery when aiding someone with a whip (if your GM allows you to use Bodyguard with whips), as they do cause attacks of opportunity when used.
Using a whip provokes an attack of opportunity, just as if you had used a ranged weapon.
