It depends on what one means by “invalid”.
First of all, “invalid transaction” and “invalid address” are not exactly the same.
Mining nodes are responsible for checking the validity of the transaction, including its scripts, but they do not check the validity of the human-readable output address string; that validation is primarily left to wallet software.
These two are different because, if a wallet somehow allowed a transaction to be created using a invalid address (bypassing a checksum failure, for example), the resulting transaction would be considered “valid” by the network if the ScriptPubKey created from that mistyped data is syntactically well-formed according to script rules, even if it locks funds to an unrecoverable or unintended condition. The transaction isn’t invalid by network rules, but it’s a problem for the user unless that is exactly what the user intends.
A purported burn address can be fake. There are addresses that might seem “invalid,” but are not. If the address passes the sender’s wallet, and the transaction associated with that address passes the validation of the mining nodes, you may not really be so sure the coins sent to the address are indeed unredeemable.
For example, an address that has a wrong checksum can pass the validation by mining nodes, who don’t validate the checksum in an address but leave that to user wallets. A transaction sent to such an address may be stopped by a standard wallet, but one just cannot be so sure that the senders are not using a nonstandard wallet (especially when senders are lured to participate in some kind of scheme, not knowing they’ve been tricked).
On the ohter hand, an address that is inherently unspendable-from, if it exists, is a genuine burn address.
But how does the public, particularly the senders, know for sure that an address is inherently unspendable-from, namely, unredeemable by its owner?
One sure case is a scenario where the owner of an address can provide mathematical proof that he does not have a valid private key for the address. But the question is, how does one provide such mathematical proof?
Well, that’s what CSW has done in his example.
In contrast to the potentially fake burn addresses, the address “1CounterpartyoThisIsAlsoAoBurnoAddr” given by CSW is a very strong valid burn address.
This is because for that address to be redeemable, its owner would have to compute almost every one of the 35 characters (because they are not random) in the address to find out a valid private key that corresponds to a public key, which, in turn, matches that particular address.
Note that the above example given by CSW is not a practical vanity address. To understand why, realize that computing a vanity address that has 35 targeted nonrandom characters is not three times harder than computing a vanity address that has 12 targeted characters. Using Base58, it is (58)^23 times harder, which is so close to infinite that it would be beyond practicality to compute.
In other words, with an address given by CSW, you are practically sure that its owner does not have a valid private key. You only need to trust the math. In contrast, in the purported burn address, you just don’t know. You have to trust the owner.