Hi @aquavivafernandes,
As you guessed above, it is entirely dependent on the web browser login/session functionality of Google Drive. In order to access and edit Google Docs in a Google account, you need to interact with it via the web browser, which means you need to be logged into the correct account. As you know, this can be a pain because of the limitation Google has in this area.
This is a big difference from non-Google Doc files, which can be accessed and edited locally via odrive across as many Google accounts as you want.