The internal clock is (I believe) multiplied to get 250 Mhz. I don't see you measuring 250 Mhz with any of the logic analyzers from this company. Maybe one from HP or similar. You would need special cables and connections to reach these frequencies.
I am retired from EE/Sensor/Mechanical development my whole career. When a design required it, we would use the more sophisticated equipment as required.
However now this is hobby and I don't wish to put too much $$ into test equipment. The reason I picked the one I linked to is, its disposable. If I accidently put too much voltage into the input and fry it I toss it and have a backup to take its place.