@Jona Santiago from what im hearing you were aware that you would be short on the needed quantity material? Was there any kind of understanding as to what boards were or were not be used?
I guess a few ways to look at it is would you be happy if he would have rejected half the boards because they were not grade A and you had to buy more?
Another thought is does it actually matter as far as functionality (shedding water) of the siding or is it only the appearance you have concerns about?
Depending on the neighborhood it may not be worth the extra cost of new boards if the existing are doing the job as I bet a lot of people will not even notice. Its difficult for me to tell by the pictures but quality of materials can have a HUGE impact on the finish product. Contractor may have assumed since you were willing to use the material in the backyard you would not be as concerned about appearance.
Personally I hate installing materials I do not have control of selecting and have walked away from projects as it is not worth the heartache of missed expectations.
Hope this helps and best of luck!