Android runs ON Linux? I bought an Android PC from Amazon and found it booted Linux then booted Android.  I mean literally booted Linux (penguins splash), then booted Android (Android splash).  I contacted the vendor asking this particular question, and he stated: 


  The mini PC has the Linux bootup first as Android runs on top of Linux


I have tried googling and searching Super User for an answer, but have so far found nothing.   I know Android uses the Linux kernel to some extent, but is that statement correct?  Is this common for an android device?

If this is a false statement, should I be worried about 3rd party applications running on the Linux OS at boot?

Device Information: Android 4.2 Jelly Bean, RK3188 Quad-core 1.6GHz CPU Cortex-A9 (28nm), 2G DDR3 RAM / 8G Flash

Link to Amazon, and supplier.
Android runs the Linux Kernel for the core system and it can be (and is) optimized for various platforms (compiled for ARM, x86, x64, PPC, etc).
Here is a fantastic graphic to demonstrate this for you:


Source: Post on Unix.SE
Android relies on Linux version 2.6 for core system services such as security, memory management, process management, network stack, and driver model. The kernel also acts as an abstraction layer between the hardware and the rest of the software stack.
Source: http://developer.android.com/guide/basics/what-is-android.html
And my comment on your second sentence is that Linux Kernel is not meant for only desktop operating systems. Its use cases vary from Desktop OS to Servers, mainframes and supercomputers to Embedded Devices.
Linux is a widely ported operating system kernel. Due to its low cost and ease of customization, the Linux kernel is used on a highly diverse range of computer architectures: in the hand-held devices and the mainframe Systems, in devices ranging from mobile phones to supercomputers.
On the other note: Palm (later acquired by HP) use Linux-derived operating system, webOS, which is used into its line of Palm Pre smartphones. Several network firewalls and routers from makers such as Cisco/Linksys use customized linux kernel. There are tons of devices out there which are using embedded linux.