There are a couple of points being bounced around here.
1) What is a species?
2) Has speciation taken place amoung finchs of the Galopagos?
1) Since speciation is a gradual process in many cases it can be difficult to decide then the line has been crossed. Until there is a reproductive barrier speciation may not be clear. However, for any number of reasons (historical, convenience, genetic) a species may be declared. It is the classic lumper and spliter argument.
2) Given that speciation may start and not complete it is possible, as you sources note, that it could reverse. It seems that the experts who are argueing over this have somewhat fewer species than once upon a time but still more than one.
I don't see why this is such a large issue. Cases like this aren't too surprising and there are lots of cases here a reproductive barrier does occur and full speciation takes place.
For now we have a number of finch species. Only by settling on a defintion and applying that to the populations there with enough data gathered are we going to be satified that we have the 'right' number and be able to know if the number if changing up or down.
(from a previous post)
The third objection I am not familiar with. Does it apply to birds?
Yes it does. The first case of this I heard of I learned about here. There are such a series of gulls around the north pole.