Who benefits from the 'enhancement' and who bears costs, may explain labeling.

From a technical perspective, species recently (e.g the past century) immigrated from another continent may be labeled as (alien) invasive.

I think it comes down to the term used and perhaps more care would clarify the point you are making . Non-native or introduced does not necessarily imply a negative impact (some species as you say can complement existing communities). Weed or invasive on the other hand does imply a negative effect - the former is particularly applied to economic/agricultural systems, the latter to the impact on natural systems (although of course weed is a broader term used in any situation). There are protocols for assessing how invasive plants are ) ie not all weeds/non-natives have invasive characteristics (see link for example protocol), so not helpful to use term invasive without this attribute being established.

http://www.hear.org/Pier/

I think the labelling just depends on the labeller's perspective and insight. I was puzzled when I heard my neighbour saying to her friend "These strange weeds just invaded her garden" as she pointed at my front garden. She was refering to my vegetables that I had interplanted in my flower garden as 'strange weeds'. OMG, she almost root some off the garden, if not of my timely intervention. She is a lovely neighbour who is ready to give a helping hand in my garden at anytime. Beauty lies in the eyes of the beholder ...

Indeed, it is very true that many species get labeled weeds or pests that are actually great healers and restorers of ecosystems and lend greater balance!

There are many ecosystems so degraded by humans that we should be thankful in many, thought not all cases, that there are at least some plants and animals that can come in to reestablish life communities here.

A published example (Lantana camara) supporting Craig's claim. 

Article Mid-altitudinal vegetation of the Macaronesian island Santo ...

Thanks Hein. Good case in point