Non-Bitcoin blockchain security questions
Ethereum is one example of the blockchain used to store the contract transactions. Nodes on the blockchain validate the transactions and add it to blockchain. Ethereum also has it's currency and miners are rewarded for doing work. What you think is absolutely right, if you don't have any incentive mechanism in place then only few people will mine and network can easily be attacked. 
When companies talk about using blockchain for only themselves, they are referring to private blockchains and not public. Node needs permission before they can join this private blockchain thus not prone to attack. Otherwise in public blockchain anyone with 51% majority can easily alter the transactions. Some attacks are possible even at 33% majority.