It’s a bit more complicated than that unfortunately. RCS wasn’t made by Google, but they did join the GSMA that manages it. They are pushing it as an alt/war against iMessage, but it doesn’t go through their servers as far as i know, it’s still a Mobile Operator service (like SMS), so it goes through your provider (and I guess Google’s if you use Google Fi).
I kinda think the smart thing for Apple to do is to implement RCS support (make the bubbles orange/purple or something) and then they’ve done it and can continue working on iMessage if they like.