In earlier versions of Moodle (2.0 -> 2.forgot when) that was true. You linked to a google doc and it was copied to storage in Moodle. Not desired. So corrected. Most recent versions of Moodle there is a check box that has the effect of NOT copying it to Moodle filedir.
A better way might be linking to Google docs, is URL. The Google Doc, of course, has to be set up for sharing ... to a list of folks, to members of your own entities Google Domain or Read only for anyone with the link (which, I assume, would only BE in your Moodle course). It goes without saying that whatever is shared a certain way isn't totally protected.
Google can change the rules, however. They can 'giveth' and thus they have the right to also 'take away' ... especially if it's 'free'. And they have, in the past, done such things.
There are limitations to videos and other such documents in Google. They have a max ... see the last link below. Many teachers using Moodle and linking to videos/etc. never see that cause the number of students involved are not close to that number. So I'd say it's not a place to store and use videos (other files) for a Moodle course that has a large number of students accessing the link to the video.
Since I was talking videos:
Can't seem to find the Google page that explains the restrictions as to hits per, etc. but it's out there somewhere.
Naturally, one has to 'Google' for it ... but
Still though ... for videos, other services exist that might be better (overall). Rare, though, they would be 'free' and even if they were, they also have to the right to 'taketh away'. Enjoy 'free' while you can and as long as you can. But, be prepared for alternatives to free.
Hope that helps some ...
'spirit of sharing', Ken