BLUR airdrop claim explained - embedding a proof into a transaction

Question

Recently, I saw that Blur had a twitter dependent airdrop. So basically you had to tweet and then you would get the option to claim tokens. I went to analyze the code, but it is overwhelming for me.

This is the claim function:

function claim(
        address account,
        uint256 amount,
        bytes32[] memory proof
    ) external {
        bytes32 leaf = keccak256(abi.encodePacked(account, amount));
        require(!claimed[leaf], "Airdrop already claimed");
        MerkleVerifier._verifyProof(leaf, merkleRoot, proof);
        claimed[leaf] = true;

        require(IERC20(token).transfer(account, amount), "Transfer failed");

        emit Claimed(account, amount);
    }

This is the Merklee Verifier:

pragma solidity 0.8.17;

/**
 * @title MerkleVerifier
 * @dev Utility functions for Merkle tree computations
 */
library MerkleVerifier {
    error InvalidProof();

    /**
     * @dev Verify the merkle proof
     * @param leaf leaf
     * @param root root
     * @param proof proof
     */
    function _verifyProof(
        bytes32 leaf,
        bytes32 root,
        bytes32[] memory proof
    ) public pure {
        bytes32 computedRoot = _computeRoot(leaf, proof);
        if (computedRoot != root) {
            revert InvalidProof();
        }
    }

    /**
     * @dev Compute the merkle root
     * @param leaf leaf
     * @param proof proof
     */
    function _computeRoot(
        bytes32 leaf,
        bytes32[] memory proof
    ) public pure returns (bytes32) {
        bytes32 computedHash = leaf;
        for (uint256 i = 0; i < proof.length; i++) {
            bytes32 proofElement = proof[i];
            computedHash = _hashPair(computedHash, proofElement);
        }
        return computedHash;
    }

    function _hashPair(bytes32 a, bytes32 b) private pure returns (bytes32) {
        return a < b ? _efficientHash(a, b) : _efficientHash(b, a);
    }

    function _efficientHash(
        bytes32 a,
        bytes32 b
    ) private pure returns (bytes32 value) {
        assembly {
            mstore(0x00, a)
            mstore(0x20, b)
            value := keccak256(0x00, 0x40)
        }
    }
}

My theory is that each time a user tweets, the website recognizes this and embeds a special proof in the transaction, which is then computed with the amount and address and finally verified with the root proof(the only owner function). What I don't understand is why can't this system be cheated? Can't we just copy one of the proofs into the transaction and avoid the twitter verfication?