I'm sure both sides are as bad as each other on the competition aspect, after all it's Elon Musk and Amazon/Bezos, I can't imagine two worse people for that. But it does seem a little unfair that Amazon have barely any proven track record and could prevent SpaceX from furthering their very proven track record.
Edit: as much as Blue Origin may play into the plans for this, they have not reached orbit, and do not have an operational rocket suitable for this (yet). Maybe Amazon have signed a deal for launches, but otherwise just being owned by the same eccentric billionaire shouldn't really suggest the ability for the company to pull it off.