Windows Server cluster failover and adapter teaming are tested together by Intel, and this configuration should work. I notice that the driver versions recorded in the thread on serverfault.com are a few years old. Are you using the latest drivers and ANS (teaming driver)? You can download the latest drivers and software, version 17.4, from http://downloadcenter.intel.com/Detail_Desc.aspx?DwnldID=21228.
The thread on serverfault.com appears to be related to using IPv4, so I will assume that is the IP version. If you are using IPv6, let me know.
What are the models of your Intel adapters? This might not matter since the issue seems related to teaming, but then again, there could be something specific to the NIC or NIC driver.
The whitepaper at http://www.intel.com/network/connectivity/resources/doc_library/white_papers/254031.pdf explains details of how the ALB/RLB team works. For receive load balancing, the driver uses ARPs to balance responses to the MAC addresses of the team members. If upgrading to the latest drivers (from the 17.4 package) does not resolve this issue, try turning off the Receive Load Balancing (RLB) option that is available as part of the ALB team configuration. Let me know if disabling RLB makes the problem go away.