The thing is that the help action is in two sections, one general part and a combat part:
- General part: Sometimes two or more characters team up to attempt a task. The character who’s leading the effort — or the one with the highest ability modifier — can make an ability check with advantage, reflecting the help provided by the other characters. In combat, this requires the Help action (see chapter 9, “Combat”). A character can only provide help if the task is one that he or she could attempt alone. For example, trying to open a lock requires proficiency with thieves’ tools, so a character who lacks that proficiency can’t help another character in that task.
- Combat part (referenced by the general part), the Help Action: You can lend your aid to another creature in the completion of a task. When you take the Help action, the creature you aid gains advantage on the next ability check it makes to perform the task you are helping with, provided that it makes the check before the start of your next turn. Alternatively, you can aid a friendly creature in attacking a creature within 5 feet of you. You feint, distract the target, or in some other way team up to make your ally’s attack more effective. If your ally attacks the target before your next turn, the first attack roll is made with advantage.
Since the general part is in the "Using Ability Scores section", it is meant to refer to just that, and deferring to the combat part for the more specific rules of helping in combat. The Help Action is more specific, therefore takes precedence, and is not about an ability check anyway, it's "Alternatively, you can aid a friendly creature in attacking a creature within 5 feet of you" and doesn't require being able to attack.
This has been clarified in Sage Advice and included in the Sage Advice Compendium which is part of the official rules anyway.
That does not mean that you cannot rule otherwise, but the official RAW are (now, since the SAC is part of them) clear.