I feel this is on topic as it relates to you using Google services without payment.
This isn't information sharing, this is using a service which has costs (hardware, software, employee time, power, cooling, etc...). You are using the ReCAPTCHA service. If you don't pay them for that (either in time or in money) then in my opinion you are stealing the cost of that service.
Just like how if you got a taxi, then just walked away without paying. Yeah, you aren't stealing any physical goods, but you are costing the taxi company something and you aren't paying for it. And if you agreed to get a free taxi ride in exchange for washing their taxi car for them, and you just walked away at the end, that would be stealing in my eyes.
Using the reCAPTCHA service lets them use the data from it for machine learning. That's the reason they are providing it for free, and if you attempt to use the service without paying (or in your scenario maliciously provide false information, which not only doesn't contribute, but can mess up the results from those who do), I feel you are stealing it just the same.