You’re taking a lot of flak for this so I’ll try and back you up a bit.
Not all workers are equivalent, and not all roles that seem the same even in the same team, actually are. Let’s say we have a team of 10 people, each with slightly different experience and skills. One of them finds another job with higher pay and asks for it to be matched. What do you do?
It’s quite possible this other role actually matches their skills better than the one with you does. Maybe they are actually worth more to this other company than they are to you. Maybe they had other reasons for looking for a job aside from pay, maybe they’re tired of the job or want a fresh challenge. Maybe it’s a combination of all sorts of factors. Pay is only one.
If you do increase their salary, what about the rest of the team, do you pay them more too? Do they all have the attributes this other company valued in the person they made the offer to? Would they have all got the same offer? Probably not, but now you’ve upped the going rate for a member of your team. They will want the same.
It’s just a really messy situation to get into. If staff retention and recruitment is a problem or you don’t want it to become a problem then sure, of course you should make sure your compensation rates are fair. Of course under paying your team will cause problems. But one person getting one job offer doesn’t necessarily mean anything, except for them.