Zero byte header in RSA-OAEP vs. RSA-PSS
I think it actually is, lets read through chapter 8.1.1 Signature generation operation:


EMSA-PSS encoding: Apply the EMSA-PSS encoding operation (Section
9.1.1) to the message M to produce an encoded message EM of length
\ceil ((modBits - 1)/8) octets such that the bit length of the
integer OS2IP (EM) (see Section 4.2) is at most modBits - 1, where
modBits is the length in bits of the RSA modulus n:  

    EM = EMSA-PSS-ENCODE (M, modBits - 1).

Note that the octet length of EM will be one less than k if
modBits - 1 is divisible by 8 and equal to k otherwise.  If the
encoding operation outputs "message too long," output "message too
long" and stop.  If the encoding operation outputs "encoding
error," output "encoding error" and stop.



Now the sentence "Note that the octet length of EM will be one less than k if modBits - 1 is divisible by 8 and equal to k otherwise." clearly indicates that this is similar to OAEP encryption.

Furthermore, if you look at the encoding operation in 9.1.1:


11. Set the leftmost 8emLen - emBits bits of the leftmost octet in
maskedDB to zero.

12. Let EM = maskedDB || H || 0xbc.



You'll see that the leftmost (most significant bits) are set to zero.