Do small preamp tubes 12ax7 need to be matched?

12AU7s are to be avoided.  In my experience, any other equivalent tube (12BH7, 6CG7, 6FQ7, even 6SN7 if you can change the socket) will sound superior to a 12AU7, in a gain topology.  This does not apply to cathode follower or phase splitter use (in an amplifier; preamplifiers don't generally incorporate a phase splitter).  In those latter cases, the 12AU7 is "OK".
I am aware that the Herron allows optional use of 12AX7/12AT7, so that the gain can be modulated thereby.  I have wondered how Herron gets away with that without a noticeable difference in SQ, at least according to its many admirers. Are there switches that must be re-positioned, for one tube choice vs the other? 12AT7s can be operated on relatively low current, so that parameter can be chosen to be compatible with a 12AX7.  But I have always felt they sound better with a tad more current than can be tolerated by a 12AX7.  Just one man's opinion based on some experimentation.
Mulveling, By "phase inverter", do you refer to what is also called a phase splitter?  In that case, I can easily believe that the 12AU7 could sub for the 12AX7.  Although the operation of the 12AU7 might be improved by increasing plate current.

It might be that in the case Chakster cites, the tube is used as a cathode follower. Or a phase splitter.

You can "use" a 12AT7 to replace a 12AX7, in that the pin connections of the two tube types are identical, but that would be far from ideal.  The 12AT7 has less gain, a lower plate resistance, and a higher transconductance compared to a 12AX7.  In a phono stage, the difference in gain would be quite noticeable, even with high output cartridges, if one were to replace a 12AX7 at the phono input with a 12AT7.  But also the 12AT7 would function suboptimally in a circuit designed for a 12AX7, so there might also be noticeable distortion.  (I am qualifying my statements, because I know someone is going to claim that he used a 12AT7 in this fashion and it sounded wonderful.)

Mulveling mentions encountering 6SN7s where one triode tests like new and the other triode tests like its near death.  (The 6SN7 is a dual triode, with two completely independent triodes in a single glass envelope.) This can happen with a tube that has been pulled from a piece of equipment where only one of the two triodes (the dead one) was actually attached to the circuit.   Often equipment was built this way so that one could swap L and R channel tubes after the tubes seemed to need replacing, and thereby gain use of the unused section in the opposite channel.  

I am not a big believer in paying a premium for matched tubes, because tubes do not age in synchrony.  So after a few months of use, one of those two tubes may test quite differently from the other.