No, I do not know why you believe diodes are somehow backwards. Unlike other polar components, diodes, including zeners, are intended to operate with both forward and reverse voltages within their rated limits. Diodes have many applications and I don’t know what you consider most common. When used in a rectifier you would measure the positive voltage on the cathodes. When used as clamping diodes the positive most voltage would be measured on the cathode during normal operation. And I assume you are referring to the typical shunt regular application for a zener when you talk of them being “upside-down”, in which case you would measure the positive most voltage on the cathode. All diodes have a reverse breakdown voltage but most diodes are not intended to be operated at or above this voltage and are likely to be damaged if they are. Zeners function just like regular diodes with the exception that they are intended to operate in the region of their rated breakdown voltage, as long as they also remain within their rated current. Zeners also have a much better controlled breakdown voltage.
The idea that the anode is a “positive” terminal only holds true for LEDs and only because they only emit light when forward biased.
Edit: Part of the problem is probably due to people like Sparkfun publishing information like this.