This is true. On the night of the first wave of strike aircraft, Saratoga's airwing was coasting-in from southern Anbar province southwest of Ramadi. There was a big MiG-25 base up at Al Taqaddum to the northeast, located in between Ramadi and Fallujah. VFA-81 (Speicher's unit) was inbound to hit targets, but was equipped for limited air-air if need be. As Speicher's division was on its ingress, they were receiving AWACS indications of MiG activity (further IDd as Foxbat) approaching their formation from ahead. The MiGs blew past their formation and behind them, towards further strike and CAP aircraft also ingressing. What wasn't known was apparently one of the MiG-25s reversed course and pursued the division, eventually launching a (likely) AA-6 ait/air missile and downing Speicher's F/A-18.
What's perplexing was that it wasn't even a few hours following Speicher's shootdown that (then) SecDef Cheney was holding a press conference with the (I believe) CNO of the Navy and it was announced that Speicher's plane had been lost (not mentioning his name) and that the pilot was killed. How did they know that? There was no CSAR launched to go check the site, nor were any aircraft directed to check the area out for wreckage/fire. His exact impact point wasn't known at the time, but the general area was. That was a very, very bad call to make publically, so early, IMHO.
As a sidenote on MiG activity that night, when I was training in the F-117, we had a few civilian classroom/sim IPs who were former Bandits from the black-days of the program and into Desert Storm. One of them related how he was ingressing into a target into Baghdad on a partly cloudy, dark night with a few stars. Flying blacked out on autopilot and with his head down in the sensor display attempting to locate his target to drop his ordnance on, he feels a "presence" and a "shadow" comes into the cockpit. He looks up and instinctively ducks, just to see two Iraqi MiGs passing overhead his aircraft in a route formation about 100 feet above him from right to left....a near midair. They were patrolling for US aircraft and he watched as they passed over him, noting the ordnance suspended beneath them, and continued monitoring them as they continued to his 9 o'clock.....watching the glow from their tailpipes as his 117 bounced a bit in their wake.