Most of the bits of the right answer are here, but scattered between lots of posts.
Before dealing with the US, the general JAR position is this.
A JAR PPL may fly under VFR only. However in most JAA countries, the defintion of VMC includes flying above a solid layer. This means that a flight can be VFR and above a layer providing it is separated adequately from cloud. This in turn means that a non-IR JAR PPL is ordinarily allowed to fly above a covered layer.
The UK blurs the issue in a number of respects. For example a basic JAR PPL may fly IFR in the UK, outside controlled airspace, and providing it is done in VMC. The most relevant factor to this discussion though is that the UK has added an additional restriction to its implementation of the JAR PPL. A PPL holder without an IMC rating or an IR must always fly in sight of the surface. This means that in addition to flying in accordance with VFR (which even in the UK permits flight above a covered layer), a UK JAA PPL must be in sight of the surface. If they hold an IMC or IR, this restriction is dropped, and they may then enjoy the full privileges that other JAA PPL holders enjoy.
Now we come to the US.
There are two terms in use in the US. VFR-on-Top and VFR-over-the-Top.
What we are discussing here is VFR-over-the-Top. In FAA terms, this means a flight which is being conducted under VFR, and which happens to be flying over a solid layer of cloud. This is no problem for an FAA PPL, since like the normal JAA PPL, an FAA PPL must simply comply with VFR (the rules), and the US definition of VMC permits flight above a covered layer.
VFR-on-Top in the US is something different. This specific phrase is used to describe a form of IFR clearance, hence the confusion. Imagine an IFR finds itself flying along above a solid layer in otherwise wonderful conditions. If it sticks to IFR, it will constrained to fly at an IFR level, and may well be subject to routing constraints. If it requests a "VFR-on-Top" clearance, it may fly at any appropriate VFR level (being semi+500) so long as it complies with cloud separation requirements, but it continues to be under an IFR clearance, with the benefits that entails. When it is ready to come down through the cloud, it informs the controller, who descends it back into the conventional IFR system. To request and obtain a VFR-on-Top clearnce, an FAA PPL must hold an IR.
Hope this helps
2Donkeys