This is a rather specific best-case scenario that involves these factors: one of the top two quarterbacks in the draft (Teddy Bridgewater or Blake Bortles) being available at 19, followed by the Cleveland Browns being in need of one.
For this to work in said scenario, the Dolphins will have to put on their absolute best poker face and try to convince the Browns (and the NFL) that they're not 100 percent certain that Ryan Tannehill is the guy, while the Browns will have to draft another position in order to be in need of a quarterback.
The second part could certainly happen, as this draft class really doesn't have a quarterback that should go in the top five (some would go so far as to say top 10, but I'm not going to stretch it that much). Picking fourth, the Browns should certainly be able to draft one of the three best players in the draft (Jadeveon Clowney, Khalil Mack and Sammy Watkins) and hope that a quarterback falls to them.
How possible is it that Bridgewater or Bortles could be available at 19 is another story, but as Omar Kelly of the Sun-Sentinel explains, "it is a strong possibility one of the draft's first-round quarterbacks will be there when Miami's on the clock on May 8th."
This leads to the first part (and I'll include Fresno State's Derek Carr as one of the first-round picks as well since, if anything, he's the most likely quarterback to be available at that point), which will be difficult for the Dolphins, since it does seem rather clear that they do believe in Ryan Tannehill.
If Bridgewater, Bortles or Carr are there at 19, it will be in Miami's best interest to Hollywood it, and I'm fairly shocked that they haven't invited at least Derek Carr down for a pre-draft visit, which is something that could help them in said situation.
Why is this the best-case scenario? Simple: more draft picks. This is a good and deep draft, especially at some of Miami's real positions of need (offensive line and linebacker are the top two), and it would help the Dolphins if they could get at least an extra pick in the first three rounds.
A trade down with Cleveland could do that, as it would likely involve the 26th pick (Cleveland's second first-round pick by way of Indianapolis) and the Browns' third-round pick (the 71st pick).
No other team in the first round with such a pronounced need can offer anything similar to that.