A block with reward different from the current correct reward can not be valid. Doesn't matter if it's 1 Bitcoin more or even 1 satoshi less, if it's not precisely what it needs to be, such block is invalid.
This is not accurate.
The constraint set by the protocol is that if you sum all the outputs in a block, that number must be less than or equal to the sum of all the inputs in a block and the block reward. This effectively sets an upper limit on how much a miner can reward themselves for finding a block, being the block reward plus the total fees. However, there is no lower limit. Miners are free to claim 1 satoshi less, 1 bitcoin less, or indeed, no reward at all, if they so choose. This has happened many times in the past, usually by mistake, but has resulted in the irreversible loss of a few dozen bitcoin.