It does make sense. The mercenaries probably are mostly hired to deal with pirates, so their ships and skills are basically hard counters to the pirates' own advantages.
"I swear on my pride" she says. No, she swears on the fact she knows the mercs would make damn sure to gang up on her ship and take her down with them if she puts them in a fight-or-die situation.
I especially like that he brought up how they could go commissar on the mercs right after she said they can withdraw but that it would "be a problem". He completely cornered her by giving an implication to her words. He also established himself in a sort of leader-like position by speaking out for the good of all the mercs present. I don't know if this mangaka will notice this, but it's how I see it. Also, this makes it less likely for the navy to just wipe out the mercs with the pirates, say the pirates did it, and not have to pay them.