miners validate 3 things about other miners work:
a) that previous coins have the correct difficulty at the time of mining
b) that none of the transactions are double spends of previous transactions
c) that the input values are >= the output values (input > output means balance is fees)
[...] validations a) and b) are still validatable by miners even though the coins are committed.
Not clear to me how you can do (b) when you can't see the input and output values.
It was described how that works somewhere in this thread. The short version is that the commitment contains SHA1(SHA256(public-key)) and a normal address is a different hash addr=RIPEMD160(SHA256(public-key)) and any public (non-committed) transaction reveals the public key (because that is necessary to validate signatures, and transactions contain a signature from the address public key), then if a public spend is done anyone can calculate the commitment based on the public key.
If another committed transaction is made RIPEMD160(SHA256(public-key)) is reused.
The actual details are a bit more complicated to prevent various attacks and corner cases but the above explains why you could prevent double spending of something you cant even correlate unless it is double-spent.
Adam
