I think the former
First Presidency message of Dec 13, 2004 (quoted earlier) covers these topics pretty well. If they would like to make an exception for ymyw.org, or any other site, then they are certainly entitled to do so. Even on a case by case basis. I have every trust in their judgment.
The problem with 3rd party websites is that no matter how secure they think they are, stuff happens. Every single week there are reports of personal confidential information being exposed to the public. Medical records, personnel files, educational histories, even military records. Some are exposed by accident, some by negligence, some by hackers.
Don't forget there are also website owners and administrators that will have unlimited access to the entire gammit of information stored on their website. Do you even know who these people are? Do you trust them? Can you be certain they aren't in the data harvesting business, or (heaven forbid) predators? Do they REALLY take data security seriously, or just give lip-service with a wonderfully written Privacy Policy?
My point is, once the information gets stored outside of the Church's careful watch, they have little or no control over it's safekeeping, but might still be liable for protecting it. That's not a good situation to put yourself in and I can fully understand their concern.