That is a sound policy. I'm guessing that these congressmen have quite a few bills to vote on- so it may be physically impossible for one person to read line by line each and every bill. Still, it would help to be familiar with the more salient points of each bill.
The answer to this dilemma is simple, they should not vote on any bill that they haven't read, or they vote no on it if it comes up for a vote. I don't care how many bills are shoved in front of a congress critter, if they haven't read it then the right thing to do is vote it down.