Consoles don't use Mantle. PS4's low-level API is called LibGNM and the Xbox One uses a special DirectX version
I think it was said that AMD had extensive hands-on with the console APIs, and had learned a heck of a lot working with Microsoft on the customizations on their console DX. The XBONE API is basically a special version of the 11_3 feature level, which is why DX 12 isn't going to bring a significant boost to the XBONE as it will to consoles.
And Mantle came to be due to DICE pushing strongly for such an API, and AMD saw it as a good opportunity. So together they used what a developer wanted with the experience AMD gained working on lower-level features. And there is nothing to say that DICE's push hadn't occurred prior to, or during the development of the XBONE's DX API, and perhaps was part of what helped drive the specific features within that API. I don't know if they did or not.
But it is highly likely that Mantle development began prior to DX 12 development, because it was DICE that wanted a significant change to the arena, and otherwise would have known DX12 was happening as they are a major developer that would be partnered with Microsoft for developmental feedback.
Due to that, it is quite likely that AMD had brought a lot to the table during early DX 12 development and during the setting of design goals. The manufacturers ARE very much involved in the process, so this is a likely proposition.
AMD wouldn't be afraid of getting DX12 out to the masses to "compete" with Mantle, because I highly doubt AMD nor DICE would have wanted a custom API battle between different manufacturers. This, based on how it developed, really seems like more of a push to the industry, so they got something out there as a stepping stone, and encouraged the industry partners to pursue the route on the universal stage.
Mantle wasn't ever about AMD-specific feature set for marketing/market share, it seems foolish to have positioned it in such a way. It was about advancing the industry. Thus, their having contributed Mantle to Kronos's Vulkan API so that much of what made Mantle what it is has found its way into an open-source multi-platform low-level API. And again, it's quite likely some of Mantle, or at least the overall concept of the code, found its way into DirectX with AMD and Nvidia working together with Microsoft.