The OP's RM database was at
which is on the local C: drive. That's how these things all work. I could be wrong, but I don't think that there is a cloud sharing service where the data is "all in the cloud" rather than being "local and mirrored in the cloud". Being "local and mirrored in the cloud" truly is the norm.
Having said that, whether your files are really "local and mirrored in the cloud" or whether they are really "just in the cloud" can to a certain extent be in the eye of the beholder. Let's take RM on the desktop and the RM mobile app and Dropbox for example.
Even if you "don't run Dropbox" and even if you "don't keep your RM database in Dropbox", a way to get your RM database from your desktop machine to your mobile device is to run Dropbox on your desktop and to place a copy of your RM database in your local Dropbox folder. I emphasize "a copy" because this is not the RM database on your desktop that you work on. On a periodic basis, you just make a second copy of your real RM database and the second copy is in your local Dropbox folder. Then you install the Dropbox app on your mobile device and you install the RM mobile app on your mobile device. The RM mobile app can then get a copy of your RM database from the Dropbox app on the mobile device on a just in time basis and only when it needs it. So in a sense, to your mobile device your RM database can be seen to be be "in the cloud".
Let's suppose you have three desktop/laptop computers (say two Windows and a Mac) and four mobile devices in your house - your iPhone and iPad, your spouse's iPhone, and your child's iPhone. You can install Dropbox on all seven devices. And let's suppose you put "all your data" into the local Dropbox folder on your three desktop/laptop computers. By default, "all your data" will be local to all three desktop/laptop computers all the time. The four mobile devices don't have anywhere near enough storage to contain all your data all the time. But you can look at any of your data in your Dropbox folder on any of your mobile devices, provided it's a file type that your mobile devices can understand. For example, my iPhone can display things like JPG files and DOCX files (Microsoft Word files) and lots of other file types just fine. And if I have the RM mobile app installed, I can display RMGC files just fine on my iPhone. But unlike on my desktop/laptop machines, the files aren't really on my iPhone until I need to look at them. When I need to look at them my iPhone, the Dropbox app on my iPhone makes a local copy on my iPhone, getting the copy from the cloud.
And just to confuse things, Dropbox on the desktop/laptop has options (NOT THE DEFAULT) where some or all of your files are not really there until you need them, either. But if you open a file that is not really there, you are not reading the file to and from the cloud. As a part of opening the file, Dropbox syncs the whole file to your local hard disk before the file can used. I keep saying Dropbox because that's the one I use. I also use OneDrive and it works the same way. From everything I have read about Google Drive I think it works the same way. And I think all of them work the same way. Nothing is really read or written to and from the cloud. Everything is written to and from a local folder. The files are either in the local folder all the time or just in time, and the default is usually all the time on desktop/laptop devices and just in time on mobile devices.
I understand not trusting Google. If you don't trust Google, do you trust Microsoft with OneDrive? Do you trust the Dropbox company with Dropbox. Do you trust the Idrive company with Idrive? If you want to share your data across all your devices like this, you will have to trust one of them. I mostly trust Dropbox but even so I run a piece of encryption software called BoxCryptor which works well with Dropbox and several of the other cloud sync services. Most of my Dropbox data is not encrypted, but all my personal financial data that I keep in Dropbox is encrypted.
There are indeed "fully in the cloud" services, but I don't know of any that store files per se. Doing so would simply be too slow. For example, ancestry.com itself without TreeShare to RM is sort of a "fully in the cloud" sharing service. You can create a tree at ancestry and fully share that tree with your spouse or cousin or sibling and all of you can work on the same tree. I'm not sure how ancestry works if more than one of you is working on the tree at the same time, but I think it works. But it works because it's not a Windows or Mac file that is being shared and there are not multiple copies of the data. There is only one copy of the data and it's at ancestry. The app at ancestry works out the sharing aspects of working in this manner and none of the data is synced with a file on your local device.