Andrew,
I'm not sure who says that your data will be corrupted, that's one complaint I haven't heard. IMO the problems are mostly related to operational behavior, failure modes and resource contention.
By running over NFS you introduce latency into your IO; MySQL can be particularly sensitive to such things. Now, if your network may be very fast and low latency and everything will work great, but now what happens when someone else in your environment starts doing a massive backup and fills up bandwidth on a link that your NFS traffic must use? The result will be degraded performance for your databases.
The NFS device itself becomes a new thing to fail. If it does, then all databases which use it will be unavailable. You can try to make this device more reliable in many ways, but now your operations depends on how well you understand this other system.
Also, if you have many instances running on on NFS device, what happens when your production environment starts sending a lot more queries or a really IO intensive pattern of queries? They compete for resources now; if one does a lot of IO, it can slow down others, which makes your load issue worse at an innopportune moment. You wind up with the potential for cascading type failures.
-Gavin Towey