So in a blockchain, it's straightforward to verify whether a block contains only valid transactions or not (in the sense of an address only being allowed to spend coins it really has for example). Any node running the reference implementation will reject any block that is invalid regardless of mining.
The issue with one actor controlling over 50% of mining power is that they can spend their money, then go back in time to before the spend to create an alternative chain. Since they control the majority of hashpower, their alternative chain catches up and ultimately becomes the reference chain in the view of the nodes in the peer to peer network. The bad actor is then free to spend the coins from their original transaction again, despite presumably having already received the goods or services from the original transaction.
The real innovation of the blockchain is that it solves the Byzantine Generals problem in the case where less than 50% of the hashpower in the network belongs to coordinating bad actors. In the absence of that level of centralization and collusion, you can be sure that nobody is cheating.
The issue with one actor controlling over 50% of mining power is that they can spend their money, then go back in time to before the spend to create an alternative chain. Since they control the majority of hashpower, their alternative chain catches up and ultimately becomes the reference chain in the view of the nodes in the peer to peer network. The bad actor is then free to spend the coins from their original transaction again, despite presumably having already received the goods or services from the original transaction.
The real innovation of the blockchain is that it solves the Byzantine Generals problem in the case where less than 50% of the hashpower in the network belongs to coordinating bad actors. In the absence of that level of centralization and collusion, you can be sure that nobody is cheating.