This is might be an unpopular opinion, but I have no problem with people asking for help with loading/unloading a truck, even if they really can afford to hire movers or when they may be pocketing a little extra cash from an employer. I figure that those who are willing to help out will and there is no harm/shame in receiving help in the future.
I also think that it's not just about the physical labor, but the fellowship that can occur during those moves. Especially when moving to a new ward having a group of people show up to help unload sends a really warm welcome message in a way that will be difficult to replicate otherwise. Several years ago two families moved into our ward about the same time, both families asked for help unloading. For Family A only one person showed up to help, although they didn't complain it was clear it hurt their feelings to some degree that so little help was offered. For Family B 7 or 8 people showed up. Family B instantly had friends and people in the ward they at least recognized and had some sort of connection to. Family A on the other hand didn't feel as welcome and had a harder time making friends. The wife of Family A eventually stopped coming to church. Obviously there were many other differences between the two families, and the wife made her own decision to stop attending, but I've often wondered that if they had felt the hand of fellowship right from the get go would things have turned out differently for them.
Having said that I agree with much of what unctoothman said and others in his thread. I don't want to rehash everything that was said, there were many valid and good points given. I just wanted to give my opinion that sometimes helping others move isn't a bad thing and perhaps shouldn't be considered a burden or viewed with a stigma.