If investigating his old boss is an attractive choice to Egrimm, then giving Egrimm the option becomes a matter of giving him agency.
If investigating his old boss is not attractive for Egrimm, then 'giving Egrimm the option' becomes a matter of his new boss trying to pressure him into getting entangled in political games against a person he'd rather not go against. Refusing a 'request' from your boss is never easy.
...
To pick an admittedly weird example... think about asking someone on a date.
If they are interested, or at least not disinterested, in exploring the possibility of a romantic relationship, then giving them a conspicuous, direct opportunity to say "yes, I would like to pursue this" by asking them on a date? Good idea.
But if they are genuinely not interested, or if the circumstances would make them feel pressured to accept even if one says "no pressure..." Well, then 'giving them that opportunity' becomes a very unwelcome and even creepy activity.
Which is why asking someone out is actually kind of a big deal and there's all kinds of anxiety associated with it. And why it can make a pre-existing relationship dynamic between two people become, for lack of a better term, weird. And why we have conventions that there are entire categories of people you probably shouldn't ask out because of problems with the power dynamic or something.
And you can't bypass all of that by saying "no, I don't mean it like that, I totally respect their choices and want to give them agency."
It still has the potential to make things awkward as all hell, if nothing else.