Why is Microsoft scared of Chromebooks?

Isn't that pretty much the concept of Windows 8.1 and the devices that include it -- integrates with Microsoft online accounts (like Chrome with Google accounts), defaults to storing documents in SkyDrive unless you override a default installation option, has an online app store which supports apps that are essentially web apps with some proprietary platform-specific APIs (HTML+JS Windows apps, like HTML+JS Chrome apps) and also those using other, less standard (for web client) technologies (C#/C++ Windows apps, like PNaCl Chrome apps), and main end-user and developer apps -- e.g., not just Office, but also, e.g., VS 2013, including the Express Editions, are bundled with online subscription services tied back to Microsoft Accounts.

With Win 8, they even tried, on the low-end, to offer lower-end, more Chromebook-priced machines that would cut the Windows desktop legacy that is outside of this strategy with WinRT, but so far that's been a failure -- but not because they didn't try.

> All that might be at odds with their current Surface Pro strategy though.

Doesn't seem to; the Surface Pro subsumes the strategy and extends it by moving offering a premium form factor (tablet convertible), but they've got plenty of hardware partners offering more basic, lower-priced options. They're still mostly priced more than the lowest-end Chromebooks.