Is it possible to run PIC16F88 at 3V?
As others have stated, the datasheet is indeed the LAW, but only the part that show the operating conditions. You are justified in distrusting broad claims in the text part of the datasheet, especially those on the first page. 

For the 16(L)F88 the operating conditions clearly state the allowed power supply voltages and clock frequency combinations.



As you can see, the non-L version is NOT guarateed to operate below 4.0 V. The L version is, but not up to the full 20 MHz that the non-L version can run. The 'sales speak summary' of this is that the 16F88/LF88 can run up to 20 MHz and can run on voltages 2.0 - 5.5V. Yeah, but that does not refer to the same part, and certainly not at the same time.

That said, when you grab a 16F88 or 16LF88 you can probably operate it (in your 20C lab environment) according to either graph, and maybe even run it at 20 MHz at 2.0V. Remember that there is never a guarantee that a part won't operate outside its documented normal operating conditions. But you do so at your own risk.