Is MAC-then-encrypt with stream ciphers secure?
As correctly pointed out in a comment, the authenticated encryption model assumes that 


the attacker knows the algorithm;
the attacker can query the encryption oracle with any plaintext $P$ (and a unique nonce $N$) and get MAC-then-Encrypt ciphertext $C$;
the attacker can query the decryption oracle with any string $C$ pretending to be a ciphertext.


No other data is available to the attacker. The assumption you made that the MAC alone is available is too strong.