Fisch is slightly wrong too.
Everybody has "first crack" but you don't receive the player unless you are the team with the highest priority to put in a claim.
And again, Washington can only send him to the minors without waivers, if they are the
only team to put in a claim.
Will link relevant CBA later. Just on lunch at work right now.
EDIT: 13.22
NHL CBA 13.22 Players Waived by Club and Subsequently Reclaimed Via Waivers During Same Season said:
When a Club claims a Player on Regular or Unconditional Waivers, and, subsequently, in the same season it requests Waivers on the same Player and the original owning Club is the successful and only Club making a Waiver claim, then the original owning Club shall be entitled to Loan such Player to a club in another league within thirty days without further Waivers being asked; provided that such Player has not participated in ten or more NHL Games (cumulative) and remained on an NHL roster more than thirty days (cumulative) following such successful claim.
The above quote from NHL CBA 13.22 details when a team reclaiming a player previously lost on waivers can send him directly to the minors or not.
NHL CBA 13.12-13.23 covers all other aspects of waivers, and details how any player that is waiver eligible must be sent on waivers and exposed to the whole League before they can be assigned to a minor league.
I think what Fisch might be thinking of is trades (
13.20 b)) which states a player claimed on waivers cannot be traded within the same season without first being offered to any other club that unsuccessfully put in a claim, with the same terms of the deal on the table.
To make a clear example of what Fisch was thinking: Adam Cracknell was claimed off waivers by the New York Rangers October 9, this season. He was then subsequently traded to Montreal for Peter Holland on November 30. That trade would not have been completed before New York first offered Cracknell to any other teams that tried to put in a claim for October 9 (whether there
were any other teams we'll never actually know unless that clause is triggered, as the League does not publish a list of unsuccessful claims).