I don't know if that's the case. Rewards have been dropping due to Bitcoin's increase and I recently deposited 80,000 from coinpot. I had no captcha before depositing that (and right afterwards too), so I don't think I've caught up in just a few days.
Check in your personal stats page and you will see the total and then compare to your balance.
Also, if it is set by Google as you say, why is it so much easier for freedogecoin and the moon sites? I'm having one screen on those sites and even if I don't do it 100% correctly I pass, but I still can't pass the one on freebitco.in. I'm not doubting you, just wondering.
From personal experience, I use several websites that use reCapcha and when I do a lot in short space of time they all get harder. What you say doesn't match what happens to me, I can't think of why that would happen to you.
As far as i can see, there are different stories for each user. I had some problems in the past, and it was so bad in fact i had to format my computer in order to fix it( i work with faucets daily, and it was a "must" for me). I believe there is a much more complicated algorithm behind this service from google. It might be measuring some other actions and circumstances in order to adjust difficulty level for each user.