BBIBH and MattMan, in some respects I agree with you. In other respects, it’s not that cut and dry. So first let’s get Mattman’s point out of the way. Lousy sound in gets you lousy sound out no matter how good the components are which follow … no argument. But in general, IMO, the source is not usually the weakest link till you are far down the upgrade path.
I think the argument being made from the other side is more about money: starting and upgrading on a limited budget. Most don’t have $5k, $10k or more to start off with a system that benefits from subtle upgrades. So upgrading a budget system the most likely path is cost driven. So what gets you the most bang for the buck when it comes time to upgrade.
First let’s define a typical budget system. Todays low end devices (I.e. receivers, cd/dvd players, etc…) are less expensive and produce better quality sound then ever before. This is because more and more functionality is being packed into inexpensive chips saving design time and manufacturing costs. Speaker components and speaker design on the other hand have not changed that much. Making it, IMO, the limiting factor in a budget system. I’d bet that a $300 receiver with $700 speakers would sound better at medium volume than a $700 receiver with $300 speakers. So, if I had to guess at the weakest link in the average budget system I’d generalize it’s the speakers.
From there figuring out the weakest link will depend on the problem you’re trying to solve. So, if the sound is being distort because you like listening at higher volume than your receiver is capable of, my first suspect would be your clipping the amp (but not necessarily the only suspect). If it’s a high noise floor you’d need to work your way backwards though the chain as it can be a lot of things (and not necessarily the device with the worst noise spec)
That said, If I had to guess at the next weakest link, after getting decent full range speaker (or adding a sub to a decent bookshelf speaker), it would be to get a decent amp to improve dynamics at volume. The reason is that an ampifier cost increases significantly with the power it can deliver. Budget is a key factor preventing most people from doing this and, IMO, it’s the first cost trade off most people make even though they might not know it (I.e. the power difference between that $300 receiver and $700 receiver, call it 75 vs 110watts, would not make a perceivable volume difference). Note the $700 receiver might be justified if it has pre-outs in anticipation of adding a future amp.
So, to sum it up in a different way … the user determines the problem to solve and the best solution may or may not be what you think it obviously is. It may not even be a component upgrade … and of course the solution is always limited by budget. | 
Just a general mutter like an old man on a park bench. Lol. 
