M&M Broadcasting in Waco has AM_1590 and runs two translators on 101.3. The call it 101.3_Bob_FM_AND_1590_A_M.
Translator rules clearly state you cannot take translator(s) and make them a stand_alone FM.
If anything, EVERY time a station ID is given, it should state CLEARLY the AM_1590. Even when you listen to JUST the AM, it's not identified.
What's up with these OUTRIGHT, flagrant violations of translator rules?
Translators rules are a little different for AM stations. For instance, AM stations that are being translated on an FM translator do not need to be fed with an over the air signal of the AM. They can be fed via an STL audio feed. Also...if the AM is a daytime only station the FM translator can continue to broadcast the programming at night when the AM is off the air.
The only time they would need to identify the AM would be at the top of the hour with it's legal ID. All they have to say is "KLRK Mexia" They could add something before that or after such as ""KLRK Mexia / Waco" or even "KLRK Mexia / Waco - Central Texas' Classic Rock Leader". Basically as long as KLRK and Mexia are mentioned together back to back they have completed a perfectly legal station identification. Anything before and after such as frequency or format is just station branding mixed into the ID.
Now if they are not broadcasting "KLRK Mexia" at the top of the hour then yes...they are in violation.
On a side note...while they could verbally announce the legal ID for the translator they don't really have to. Translators are allowed to ID themselves at the top of the hour via FSK (frequency shift keying). Most low power transmitters today that are used for translators (i.e. Armstrong, PTEK, etc) have built in FSK.