While "we foreigners" tend to think that paying up a few bucks is the easy way to solve problems, it is often the worse thing you could do if the law is, in fact, on your side. Tea money creates the expectation that more tea money may be forthcoming which then keeps the cycle going and creates more "problems that must be overcome" down the road - people talk. NEVER pay tea money if the law is on your side as the situation can and will be resolved by this person calling that person and informing them (or reminding them, as the case may be) of what the law actually is supposed to be.
Supervisors in government are usually the ones who trained the clerk and they are often on the same page (this was the case in both of our recent encounters). In addition, they work in the same office day after day and it is unlikely one would contradict the other lest they cause embarrassment. The clerk embarrassed because he/she was wrong or "forgot", and the supervisor embarrassed because apparently, they didn't know the law either or trained the clerk wrong. Now, this dynamic may be a bit different in private industry (merit motivation) as opposed to governement (entitlement de-motivation) - depends on the company.
Now, grease money (paying to speed things up) is another thing altogether, and I am all for it.

Yep, we have the law on our side and will simply have someone give them a call.