Most of the time, Remington trigger malfunctions as a result of gunk getting inside will manifest itself with the trigger sear and firing pin failing to cock in the first place, so the cocking piece will just ride the cocking cam down to fired position as the bolt handle is lowered. In order for the rifle to fire when the safety is released, something has to initially hold the sear up into reset position for the firing pin to be cocked after the bolt is closed. If gunk is inhibiting trigger lever/connector movement such that it fails to pivot back into position under the sear when the bolt handle is raised, it simply won't remain cocked when the bolt is closed. This could cause an AD as well if the bolt is worked vigorously enough.
Greydog's explanation of the trigger being pulled while the safety is engaged and the safety failing to raise the sear to allow the trigger lever/connector or lever only to return to reset condition would certainly be one cause of a rifle firing when safety is released. As GD said, this would be a faulty trigger from the get-go; in a properly functioning trigger, the safety should always hold the sear up with sufficient clearance to allow the trigger to reset itself in the event the trigger is pulled while the safety is engaged.
However, GD's scenario isn't the only condition that can cause a 700 to fire when the safety is disengaged. I've seen 700 triggers that eventually developed the fire on safety disengagement issue that left the factory dimensionally correct and were initially functioning perfectly. There are a couple of conditions that can cause this to happen even if the safety properly holds the sear up in clearance position to allow trigger reset.
One cause: as GD mentioned, the trigger is pulled while the safety is engaged, and even though the safety is properly holding the sear in raised position to allow the trigger lever to return to reset position, the aforementioned gunk that worked its way down into the housing prevents the trigger from pivoting back into reset position. Then, the safety has now become the "trigger," and when released...bang.
ANOTHER scenario where this can occur:
1. Rifle sits dormant and uncocked for a period of time. Being uncocked, the trigger lever is thus in forward (uncocked) position for an extended time.
2. Gunk has managed to work its way into the trigger or previous oils inside become gummy and varnish up over time, locking the trigger in uncocked position.
3. On next use of the rifle, the safety is engaged immediately after the bolt handle is raised or engaged at some point prior to the bolt being returned to battery and closed. The sear still raises up properly when the cocking piece is held back by the cocking cam, and the safety holds it in that position before bolt closure. The safety is now holding the sear cocked and not the trigger lever, which never reset in the first place and again, the safety has now become the "trigger."
Every design involves making a series of conscious tradeoffs. The 700 trigger was designed as a self-contained unit to make it easier and more economical to assemble and still have a nice, adjustable trigger pull. By having the trigger assembly as a self-contained, enclosed unit, it was easier to precisely control the geometric relationships of the sear engagement surfaces, providing a nice crisp trigger without the need for individually hand-fitting the parts and yet installation of trigger assembly to receiver involves only driving in 2 pins. The downside is that any fully enclosed mechanism is naturally more susceptible to getting debris or gummy oil films trapped inside. This isn't necessarily a "design flaw" per se; enclosed triggers are just less tolerant of contamination, and this applies to not only the Remington trigger, but many other enclosed triggers as well.
