This is only really true if you view the rest of the roster as set in stone to what it is now and that no other moves could have been made prior to signing Brown.
There are realistically 4 players on the roster that you can move to find cap space to improve the roster: Foegele, Ceci, Kulak and Campbell.
If the goal was to upgrade Ceci, moving Ceci by himself does you no good because it will be very costly to upgrade his spot. To do so you would probably have to move one or both of Kulak or Foegele as well. But Brown's signing does not stop you from doing this. In fact, it makes it easier because you don't have to now find money to replace a top six RW at the same time.
If the goal is to find a better winger than Brown, then you have to start by moving Foegele. That won't do it because all you now have is $2.75M plus the $.775M from Brown for two wingers. $3.6M total for two wingers doesn't improve on Brown and Foegele. So you also move Kulak and go with Broberg and Niemo or sign a guy at $1M or less. Now you have $5.2M to upgrade on Brown and Foegele if you want better wingers but you still loose Kulak. $5.2M would be a challenge to find two guys who as a duo would be better than Brown and Foegele and compensate for the loss on the back end.
What this shows me is that with the cap space they have in hand the only way you could find the cap space to clearly upgrade he team this year over what it is with Brown would be to find it by trading or buying out Campbell in addition to moving out one or more of the above 4. But even then the answer is probably not from free agency so you also need assets in addition to make a trade.
I've spent a lot more time than I should trying to come up with some sort of realistic way that the team could have been made better this year than they have been with the Brown signing and I just can't find it without completely mortgaging the future. Maybe that's just my own lack of imagination. So if others have a plan I'd be happy to hear it.