Q: Is it true that Windows Azure isn't compatible with Windows Server 2012 Hyper-V?
A: No, this isn't true, and this confusion stems from the difference between the virtual machine (VM) configuration and the virtual hard disk (VHD) format.
Windows Azure IaaS is running on Windows Server 2012, and there's complete compatibility between on-premises Windows Server 2012 Hyper-V VMs and Windows Azure IaaS VMs, which means a VM can be moved between on-premises and Windows Azure IaaS without making changes to the VM.
The current incompatibility is the new VHDX virtual disk format present in Windows Server 2012 that allows 64TB VHDX files. Windows Azure IaaS doesn't support VHDX at the current time (Windows Azure has 1TB virtual disk maximum size today so VHDX does not make much sense) and so VHD must be used.
This means to have full compatibility between on-premises Hyper-V and Windows Azure IaaS, you must use VHD with the VMs (1TB or less) and NOT the new VHDX format.