I'd like to share some things I have seen on my client's machine. He has a full backup database set up once a night and every four hours differential back during the work day. But at the same time ( it should be done at night) the network administrator has ran tird party software backup to copy .MDF/LDF files. When we started to restore database it throws the error that SQL Server cannot apply this bakup file to the full backup file created at night. We did lots of testing on the developing machine and did not het the error. And only when we asked the net.admin not to run this software then we were able to restore the database succefully.
Note, I have not seen that doing LOG files backup does break the chains.
So please do lots of testing before you find your self without properly created disaster recovery strategy.
I found that MS has this KB explaining the behaviour.