Wuga already brought up this point, and it was already addressed.
The point being, we can use arbitrary time clamps to make anything look good. The '50 second' example I started with was actually intended to be more of an explanation of the math and not necessarily a comparison.
The 'real' comparisons, the 'apples to apples' as you call them, come in the next section, where you compare actually casting Invoc/RoP vs using that time to DPS with IW passive. That is the real meat and potatoes of the situation and will occur many many times during the course of the fight above and beyond the "boss is dead in X seconds" point that both you and Wuga brought up.
Basically, the comparison comes in when we calculate the 'worth' of those 3 seconds you spent casting Invocation when you could have just dpsed with them with IW passive.
The side bonus to the math is actually showing how IW is free of any time clamps, since unlike Inv and RoP it does not have a 'duration' and does not need to be 'activated' to be used.
---------- Post added 2013-03-06 at 02:49 PM ----------
As I explained earlier, you are not accounting for the fact that you actually have inherent 'downtime' for RoP and Inv since you spend time casting them. That downtime offsets the "raid wide downtime" that you are attempting to parse into the calculations.
In simpler terms.
Say you have 60 seconds of DPS time on the boss. Now you spend 3 seconds of the 60 "casting" your Invocation, then 57 seconds of actual DPS time on the boss. Due to your use of Invocation, you actually do not have 100% uptime, however, with IW since you are not casting anything, you will in fact have 100% uptime.
Edit:
I would preface that by saying, yes, if the downtime is in fact independent of "cast time downtime", then the calculation works out as you mention.
Though that is precisely the special edge case Wuga brought up. While the idea holds true, I do not think that edge case is as prolific as to warrant a general statement.
It is applicable for situations such as a boss dying, or some form of boss transition where he will become immune/unattackable after X seconds, where X is known and clamped.