The whole1 concept of magstripe data on the card is to prove that the card was present at the time of the transaction. If you were able to reconstruct it without the card, that would defeat the purpose. Likewise, that's why PCI rules require you to never store the full swipe data (so you can't replay it later). 2
If you look at what's in the swipe, you'll see that both the Service Code and the Discretionary Data fields are not printed on the card anywhere. Service codes are standardized, but there's no way to know ahead of time (i.e. without swiping) what it will be. Discretionary data is unique to each issuing bank, but usually contains information such as the CVV1 (which is not what's printed on the card), an encrypted PIN (for ATM use), and other distinguishing data. The discretionary data is also different between the two tracks.
Basically, there is no way for anyone except the issuing bank to know whether correctly-formatted swipe data is actually valid or not, but there's no way to fake it to the bank, either.
1: This isn't quite true: It's also for speed and automation.
2: The rules also prohibit storing the CVV.