ADC driver for ADC12D1600 and its common mode voltage range.

Hello.

I’m looking for ADC driver for ADC12D1600 input. This ADC has differential input scale from 0.6 to 1 V and common mode voltage +1.25 V.  

Gain of OpAmp should be between 2 and 4. Frequency band should be from DC to 1 GHz (-3 dB).  

I’m going to choose between LMH6554, THS4509. Only one thing I don't understand:

 Input common mode voltage for LMH6554 is ± 1.25 V. ADC output common mode voltage +1.25V.

So in Figure:

 

we see that for common mode voltage more than +1 V signal distortions of OpAmp are very high. The same thing is for THS4509:

Am I right to bother of this or not?

PS Of course signal distortion more than -20 dBc is not acceptable for me.