Not always, if your battery voltage was too low to turn over your engine and the other rig didn't have a "good enough" connection to your rig to deliver the required current it could still not start. And if you don't have a deep cycle battery you could have already killed your battery too by running it with a faulty alternator. It takes a lot more current to turn over the engine than it does to run the ignition and the accessories.

It is possible you bought a faulty battery, but I would be getting the alternator checked out before I put a new battery in it.

Sean