The design purpose of a inertia block in a mechanical trigger gun is to protect against fan firing or doubling.
The Browning 725 is NOT a true mechanical trigger. It clicks without recoil but does indeed require recoil force to reset the lifter to the second sear.

CT

 

Is the "click" not the sound of the hammer falling?

 

Looks like I somehow messed up that previous response and put it in the yellow box. ???

Three responses;
1. My old Rem 32 drops one, then the other, hammer with two trigger pulls, no recoil needed. It has NO inertia block, so it must be safe to consider it a "True" mechanical trigger?
2. I put a 410 Briley tube in a Browning Sporting Clays. On experienced advice, I changed the Trigger Piston Spring (not a big deal with the right tools) to Browning's 410 spring (Browning Citori Trigger Piston Spring, .410 Gauge) and it WORKED!
3. My old Citori 425 ALSO drops one, then the other, hammer with two trigger pulls, no recoil needed. It did not used to do that. I did some careful stone work on the sears then slightly lengthened (strengthened) it's Trigger Piston Spring. Now it behaves just like the Rem 32. Have not had a fan fire. I am very cautious with the 425, because I do not yet understand exactly why it no longer requires recoil to set that second sear.

Mike,

Yep the Remington 32 and it's successor the Krieghoff 32 and then K80 and both Blaser F3 & F16 are all true mechanical triggers.
I am not familiar with Citori triggers but would assume that the stronger trigger spring lifts the inertia block to a second firing position sooner and acts just like a mechanical trigger even if it started life as a inertia trigger.
Fan fires usually occur if the gun is not shouldered firmly and the gun rebounds off the shoulder with the rapid stutter of one barrel firing a fraction of a second behind the first. If that happens and you are on the target there is nothing left but dust.
However poor sear engagement can and will lead to either true doubling or a very slight delay fan fire. This is why you should never trust that a safety makes a gun completely safe because a sear could slip or be jarred out of engagement and the gun fires.

CT

 

To be certain I understand, the new K-80 triggers are "True Mechanical" triggers even though they do have an inertia block, which is there only to prevent fan firing, or doubling?

 

Recoil can cause some people to have doubles with mechanical triggers as their finger is bouncing around in the trigger guard and can hit the trigger twice. Take a look at the Blaser F3 video. It has true mechanical triggers and shows how the interia block prevents doubling.

Blaser USA: F3 Video