You certainly can ask people to sign up for Dropbox or Google Drive and a lot of folks do. It can be a bit of a side-quest if you just need them to send you a file so you can get to work on something. I've tried to make this easier to explain to the person you need a file from.
If you exceed the free tier, you'll be prompted for payment. Payment is associated with your email address, which you would enter anyway to get a link, so no additional sign-up is required. More convenient than that, I think, is that the person you are requesting a file from doesn't have to sign up for anything.
The file is encrypted in transit and at rest, but I think these are only basic measures. I agree that you shouldn't trust some guy from the Internet (including Google, perhaps). If the information to be sent is sensitive, I would recommend taking measures suitable to the level of sensitivity before sending it, probably encrypting it with keys you control rather than depending on the service provider.
Right now the size limit is 25GB, but I'm open to suggestions on that. Of course there has to be some limit, but I wanted to make it high enough that it didn't feel like there was one for most folks.
Thanks for the link. I'll check it out :)