The Dolphins ultimately did not pull off a trade, but Grier said it was his job as GM to "investigate every avenue" to improve the team's roster -- even though he used the No. 5 pick in 2020 to draft current starting quarterback Tua Tagovailoa.
Coach Brian Flores has said on multiple occasions that "Tua is our quarterback," but Grier confirmed his interest, to an extent, in any available player who is deemed one of the best players in the league.
"I don't think it's any different than any player on the roster, honestly," Grier said. "Because if there's a player available around the league that's viewed as being one of the top players in the league at any position, I think you look at it and try to go for it.
"We're very happy with Tua. We think he's developing well. Brian has been very consistent with his message, and we have been as well. He's working hard, he's showing a lot of improvement, and we think he'll continue to develop and be the player he should be."
Watson has been a healthy scratch all season for the Texans. There are 22 active lawsuits against him with allegations of sexual assault or sexually inappropriate behavior during massage sessions, and 10 women have filed complaints against him with Houston police, his attorney Rusty Hardin told ESPN's John Barr in July.
Grier said the Dolphins did "background work" and their "due diligence" into Watson and decided not to pursue a trade.
He also addressed remarks that were made Tuesday by Tony Buzbee, a Houston-area attorney representing the women who have filed the lawsuits against Watson. Buzbee said that the Dolphins wanted settlements in each case before they would pursue a trade for Watson and that either Watson or the Dolphins insisted on the women signing nondisclosure agreements.
Grier adamantly denied that the team tried to influence any decisions pertaining to Watson's legal situation.
"I think any suggestion that this organization would be dealing behind the scenes in trying to influence decisions is absolutely ridiculous and categorically false," he said. "To say that we would be involved in that is just flat wrong and it pisses me off, I'm sorry."
Grier declined to say the team wouldn't pursue Watson again this offseason, saying the Dolphins would evaluate their roster at the end of the season. However, he did say that "about 90%" of rumors and reports about an impending trade for Watson were false.
Texans general manager Nick Caserio also rebutted some recent reports but declined to comment further.
"The veracity of some of what has been reported is a little bit stretched," Caserio said Wednesday. "But that's just the nature of how these things work.
"There were various levels of discussions, specific to him and specific to other players as well. In the end, there was no trade that came to fruition, so I don't really have any comment about some of the logistics and the mechanics about what happened and what hasn't happened, what did happen."
Grier said the background work Miami did on Watson didn't reflect how the organization felt about Tagovailoa, saying "it has nothing to do with not believing in Tua."
"We never got to a point where anything was going to be realistic in terms of happening," he said. "It was still us just doing our due diligence, just talking through things. We never got to a point where anything was that close to happening."
For Tagovailoa, who said last week that he was so unfocused on the trade deadline that he didn't even know when it was, Miami's decision to pass on Watson doesn't necessarily give him any more relief now than he felt before the deadline passed.
With his team on a seven-game losing streak, Tagovailoa said his main focus is on breaking that skid one opponent at a time, starting with none other than the Texans on Sunday.
"I mean, my focus has really only been on the team that we've been playing and then obviously our team," he said. "My focus has been just what we can do better each and every day, and then throughout the week, to hopefully get us a win."