That is the general recommendation of the manufacturers. The those cards can work with a 300w as long as the components in the PC are not very power hungry. I have recommend the the Radeon HD 7750 and the Radeon HD 6670 (along with the HD 5670 and HD 4670) in the past numerous times because based on their power consumption they do in fact work with PC that have 300w PSUs.
What are the specs of your PC? If you have any Intel CPU and up 2 or maybe even 3 hard drives, then the both cards I recommended should work fine. If you have an AMD CPU, then that's a different story because AMD CPUs are power hungry and I suppose you will need at least a 350w PSU for those cards.