I'm not sure I see the contradiction.
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When a balk is made on a pitch that is a fourth ball it shall be ruled the same as when the batter hits a balk pitch and is safe on a hit or error, provided all runners advance at least one base on the play.
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So, here, the balk is enforced if not all runners advance on the 'play'.
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Therefore, with a runner on first, first and second, or first, second and third, when a balk is called on the fourth ball, the batter goes to first base and all runners advance at least one base. If they attempt to advance more than one base, they do so at their own risk.
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Here, all runners have advanced as a result of the 'play', so we leave the ball live and are not enforcing the balk.
Quote:
7.9 CALLING "TIME" AFTER A BALK
(5) If the balk is followed by ball four delivered to the batter and is caught by the catcher, call "Time" and enforce the balk unless all runners advance one base because of ball four. In that situation, play proceeds without reference to the balk.
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Here again, the only time the balk is not enforced is if all runners advance as a result of the play.
In short I suppose, is that umpires need to be aware of what happens to runners (forced or unforced) as a result of the batter becoming a runner on ball four when the pitcher balks.
How 'bout this:
In all of the following examples, F1 balks but delivers ball four to the batter.
R1, R1 and R2, Bases Loaded Balk
not enforced because all runners (including BR) advance on the merit of the play.
R2 only, R3 only,R1 and R3, R2 and R3 Balk enforced because no runner is forced to advance.
Edited (twice) to fix balk enforced sitch.