Good Logic or Bad Beat?

I wasn't exactly sure where to post this, so I apologize in advance...

Consider the following situation:

Player A makes a preflop raise with a dominant hand.
Player B makes a lousy call with a weak hand and outdraws player A on the flop.
Player B goes all in on the turn and player A calls, having also made a hand.
Player A re-draws the best hand on the river.

Question being, did A deliver a bad beat on B (having called the all-in as a huge dog), or is it fair to say that A shouldn't have been in the hand in the first place and set himself up to lose money?