My comment about AccuracyGoal->Infinity meaning that no AccuracyGoal is set was a sarcastic response to the equivalent of going into a society where nodding the head means no and shaking it means yes.
However, your points are well taken. Here's the results of following up on your suggestions.
There are no comments to any of the NIntegrate executions. Once any accuracy, preciision, working precision, and max and min recursions are set, I get the same output with no comments. The results that are plotted use ?NumericQ and is a plot of the quotent of two NIntegrate functions which have similar manitudes at about 10^(-10) units. In other words, I have normalized one function with the other. Even performing a point by point integration and normalization, the results are consistent with the parametric plots.
The integrand has no poles and, unlike some others integrals, it does not give me an excessive integrand oscillation notice. It is a multivariate integration, and I have switched the order of integration within the constraints of certain dependencies.
It looks like my anomalous results are the real results and not getting my results is the real anomaly.
That said, I have another similar set of functions that give me spikey garbage using ?NumericQ and I do get messages about the convergence. In this case, the integrand also does not have poles and I am trying to understand why the approach does not work. But that's another story.
