MySQL remote connection questions (Non-technical)

I have been chatting to several Hosting companies in regards to whether or not they allow remote access, i.e. so I and other users can connect to a MySQL DB from our local machines.

Many of them don't offer this. And of those that do, they seem (As they stress their concerns) somewhat paranoid about security owing to this.

Not knowing a great deal about Internet Apps or even MySQL, I wondered if their concerns were valid... or if all the worse could happen was whomever gets to have access can do with the data as they please. But since this would be accessed only by a VB application, wouldn't it be afforded a level of protection by whatever is set up in the app?

Finally, can anyone recommend a good host for ASP and MySQL development. (I figure its been tried and tested then :) )

Thanks for any help guys.