I'm actually unsure what grounds they're attempting this on. From the Xbox live terms and conditions (And yes, I did just read the whole lot.

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QUOTE
Please note that this contract limits our liability and we do not provide warranties for the Service. The contract also limits your remedies. These terms are in Sections 15 and 16 and we urge you to read the terms carefully.
Microsoft reserves complete and sole discretion with respect to the operation of the Service. Microsoft may, among other things: (a) restrict or limit access to the Service; (b) retrieve information from the original Xbox, Xbox 360 console, personal computer and any connected peripheral device used to log onto the Service as necessary to operate and protect the security of the Service, and to enforce this Agreement; and © upgrade, modify, withdraw, suspend, or discontinue any functionality or feature of the Service or any game from time to time without notice, which may involve the automatic download of related software directly to your original Xbox, Xbox 360 console or personal computer, and which software may prevent you from accessing the Service, playing pirated games, or using unauthorized peripheral devices.
16. WE MAKE NO WARRANTY
We provide the Service "as-is," "with all faults" and "as available." The Microsoft Parties give no express warranties, guarantees or conditions. You may have additional consumer rights under your local laws that this contract cannot change. To the extent permitted by law, we exclude the implied warranties of merchantability, fitness for a particular purpose, workmanlike effort and non-infringement.
17. LIABILITY LIMITATION; YOUR EXCLUSIVE REMEDY
You can recover from the Microsoft Parties only direct damages up to an amount equal to your Service fee for one month. You cannot recover any other damages, including consequential, lost profits, special, indirect or incidental damages.
This limitation applies to:
-any matter related to the Service,
-any matter related to content (including code) on third party Internet sites, third party programs or third party conduct,
-any matter related to viruses or other disabling features that affect your access to or use of the Service,
-any matter related to incompatibility between the Service and other services, software and hardware,
-any matter related to delays or failures you may have in initiating, conducting or completing any transmissions or transactions in connection with the Service in an accurate or timely manner, and
-claims for breach of contract, breach of warranty, guarantee or condition, strict liability, negligence, or other tort to the extent permitted by applicable law.
It also applies even if:
-this remedy does not fully compensate you for any losses, or fails of its essential purpose; or
-Microsoft knew or should have known about the possibility of damages.
Some states do not allow the exclusion or limitation of incidental or consequential damages, so the above limitation or exclusion may not apply to you. They also may not apply to you because your province or country may not allow the exclusion or limitation of incidental, consequential or other damages.
Under Condition #16 of a contract to which all parties have agreed (and if they didn't read it, more fool them) they have absolutely no case.
As further points, the terms and conditions also state that only those over 18 years of age may take any action - although I've no idea if this applies here - and the best anyone filing such a suit can hope for is a month of free live and a bill for thousands of dollars of legal fees.