Missed Base Appeal Question

[mrm21711]

I am going through my 2007 copy of the J/R manual and am slightly confused on the application of this:

In the section on appeals, under Retouch Appeals and Missed Base Appeals sections, J/R writes that: "If a suspect runner is tagged off base, there is a play and an out, but not an appeal; a subsequent appeal of such runner's missed base is not allowed."

I understand the above excerpt. He uses the example of R1 & R3, base hit to outfield, R1 misses 2B on his way to 3B, attempts to return & touch 2B and is tagged off the base by the second baseman. I understand this is NOT an appeal, the runner is out, and the R3 scoring would be a time play in this situation not a force out situation.

However, in Chapter 10 about Determining a Run, J/R gets into advantageous 4th outs that would negate runs, ect. He uses this example:

"Appeal against a runner already out: R3 and R1, two outs. R1 misses second and is thrown out at 3B for the third out. However, defense appeals and the advantageous fourth out is declared for R1's miss of 2B - no run scores since the appeal was a force out."

I am having trouble understanding the differences between the first example and the second. Both are missed base appeal situations. In the first example, is the KEY point the runner in jeopardy of being out on appeal (if an appeal was made) is trying to return to his missed base? Is that the reason there can be no subsequent appeal of his missed base? In both example, a runner who missed a base was tagged out but in the second example, the runner was not trying to return to his missed base to touch/retouch.

Furthermore (this may be redundant but I am obviously going through a brain cramp here for some reason) in the second example, what if the runner attempted to return but got himself in a rundown and was subsequently tagged out? The defense could still appeal his miss of 2B right?