reaction by adjacent unit?

I have a formerly Large Unit of Scots Pikemen (now reduced in size by archers) being charged by a Large Unit of FP Billmen. Close by are some Irish kern Skirmishers. The FP Billmen will enter their ZOC to reach the Pikemen.

Reaing the rules I can see that the kerns could react by evading or firing if they were the target but am I right in thinking that they can't react to a unit attacking an adjacent unit like this?

Opportunity Charge 5.7.3 allows a unit to react if its ZOC was violated by an enemy unit by interrupting the movement or charge of the enemy unit. According to 4.1.4, the enemy in this situation must enter the ZOC with no possibility to charge the skirmishers. This may be case, however, if the skirmishers have an impetus value of 0, they could not charge anyway, as all of the usual rules for charges still apply.

I agree that 4.1.4 (4) applies.
Reading 5.7.3 I thought, "the Skirmishers aren't trying to charge the Billmen so that's not relevant- they want to fire on the Billmen."

Ok, sorry, I only addressed charging. 4.1.4 and the reaction fire rules do not appear to permit shooting an enemy unit that simply crosses the ZOC.

Many thanks. I'm finding it interesting looking at Impetus and Baroque side by side to spot the differences between the two.
NB My Scots unit was done for anyway so even had the Skirmishers been allowed to fire 9which to me seems reasonable but the rules just don't seem to allow it) I don't think it would have changed things much!