They probably offered him a 10 team no trade clause.
Dorion had an interview maybe a year or two back discussing the Phaneuf contract. He said something to the affect of Phaneuf has a more robust NTC but we didn't sign that contract, team policy is we give out 10 team NTCs only. Then he joked about one player in the future possibly being the exception to that (lol guess not). This was probably in the 2017 off season when Phaneuf's contract was hindering our ability to protect Methot, but I don't remember the exact time line.
So it's pretty clear, this team has a policy of not giving out full NMCs. Bobby Ryan who is the biggest superstar UFA we've had to sign in the last few years got a 10 team NTC. He did get a modified NMC like policy, but that was only in relation to being assigned to the minors.
It makes zero sense to not offer Karlsson a full NMC after what may have gone down at the deadline. Even if the Sens are perfectly innocent and they were only listening as they claimed, how can they negotiate in good faith with Karlsson who would have the perception they've been trying to trade him without offering Karlsson some sort of assurance he won't be traded via a NMC?
That's completely ignoring that league wide, it's standard for a guy like Karlsson to get that. As much as Ryan is the biggest star we've had to extend in the last few years, Karlsson is maybe two tiers above where Ryan was in terms of star status.
(I am talking about Ryan as he was perceived years ago when he extended, not now that he has fallen off)