That range is total distance, not just altitude. A plane a mile away at 16,000 feet altitude is actually 16,848 feet from away from the launch site. To be out of range at 25,000 feet distance, the plane would be at 16,000' altitude, and only 3-3/4 miles away from the launch site. Wiki says max range on the FIM-92 was 26,000', so that would be 16,000' altitude and around 3.9 miles away. Also, the plane would be moving, and depending on those variables, the MANPAD would have had to have been damn near right under the plane's flight path and timed just right.
I don't discount the plane was shot down, I just don't think a MANPAD did it. If it did, they were damned lucky.
No problem if you are in a small boat off of JFK. STATEMENTS BY EYEWITNESSES
"We saw what appeared to be a flare going straight up. As a matter of fact, we thought it was from a boat. It was a bright reddish-orange color. Once it went into flames I knew that it wasn't a flare." - Lou Desyron, Flight 800 eye-witness; ABC World News Sunday; 07/21/96.
"I looked up because it sounded like thunder. I kept looking trying to figure out what it was. And that's when I saw a flare come off the water. The flare, trailing orange flame, shot up roughly at a 45 degree angle, then rapidly increased its angle of ascent. Then it appeared to strike something. This was the strangest thing I ever saw. Everyone calls it a 'missile theory,' but when you see something, you know what you see, and I didn't see a 'theory'." - Tom Dougherty, Flight 800 eye-witness; interviewed on Hard Copy, 1996''
"It was what we would best describe as a boat flare, a reddish object going up. It went up and a few seconds later we saw an explosion in the sky. I can't say if it came off shore or on shore. At first, we thought it was a boat flare. It zigzagged a little. We thought it was strange. Then, several seconds later, we saw an eruption of fire. We never heard anything. We saw a fireball, and at that point we identified what was an aircraft. We could see it fluttering down. We were the third boat on Long Island to report the incident to the Coast Guard. It was something going up to it beforehand. Yes, I saw flaming debris go down. Something attracted us to the area before it exploded. And even my wife and my oldest daughter, we all were witnesses to it. There definitely was something there first before the aircraft went down." - Donald Eick, Flight 800 eye-witness; October 20, 1997; The Press-Enterprise, Riverside, CA.
"I picked it up three seconds before it turned into a bright white ball, which split. I thought it was fireworks. And then I didn't know what to think because from the white ball, I saw two wide orange bands of light fall down, obviously the fuel igniting. I'll lay my ass on the table and tell the president or the FBI, and someone can hypnotize me: There was no way that red light was descending. It was ascending. It made contact with what turned out to be that airplane and made a white bright light and then split in two. If I were in a courtroom and the prosecutor says I've got an eyewitness, then I become a trump card. We're not just one witness but 135 or more strong. I saw something hit the right side of the plane. My opinion was it blew the wing off on impact. I assumed something went through the airplane, like behind first class and into the wing. My honest opinion, my gut feeling, is that we have the most brilliant people in the world and the best technology, [and] if they've been on scene for a year and they've not come up with something, as a critical thinker I have to ask, could they be covering up something?" - William Gallagher, fisherman from N.J. who witnessed Flight 800 crash; October 20, 1997, The Press-Enterprise
"More than 150 credible witnesses - including several scientists and business executives - have told the FBI and military experts they saw a missile destroy TWA 800. 'Some of these people are extremely, extremely credible,' a top federal official said. 'When we asked what they saw and where they saw it, the witnesses out east pointed to the west, and the people to the west pointed to the east'." - The New York Post, September 22, 1996.
"My God! Somebody's shooting at that airplane!" - Crew of a British Airways jet flying behind Flight 800 whom radioed to air traffic control; July 17, 1996.
Read at the link for plenty of others.