I'm pretty sure they did. Nintendo published the DS games in the west and had an iron grip on them. Enix didn't make this commercial:DQIX came out in 2009 - 6 years after "Enix" ceased to exist.
Squareenix only published the game in Japan alongside other games like Bravely series. They didnt want to publish it in the west for whatever reason.
Nintendo published it because SE wouldnt do it themselves. Not the first time Nintendo had to publish a game that a third party dev made. Plenty of other games made by third party devs who released the game on their own turf themselves were released WW published by Nintendo other than DQ - examples included are Ninja Gaiden 3 Razor's Edge (WiiU), Bravely Series (3DS), etc. The same in the opposite region too, like Trine 2, a western developer game, was released WW by the original publisher but released in Japan by Nintendo themselves who published it there.
If Nintendo did really have rights to the DQ series, then we wouldnt see Dragon Quest games on Playstation, iOS and Android.
DQ1, 2, and 3 are coming to PS4
DQ11 is coming to PS4
DQ1, 2, 3, 4, 5, 6, 7, 8 are on iOS and android. It wont be a matter of time before IX will come out and X too. I wouldnt doubt on XI coming either based upon the 3DS ver.
