Not if you rephrase the argument. Regarding the pebble, one might say that no matter which pebble he chose, its measurements would be unique and equally "unlikely." Similarly, no matter which universe we could ever observe ourselves in, it would have equally "unlikely" parameters enabling us to live in it.
Do you know how unlikely you are to win 10 times in a row?
The odds of you winning 10 times in a row are exactly the same as the odds demonstrated by the results of the last 10 times powerball was run.
Do you find the results of last 10 powerball runs surprising?