Not true. Instead of talking generally, let's go to the actual Florida law. Chapter 776 (Justifiable Use of Force) of Florida Statutes existed before passage of the Florida Stand Your Ground Act in 2005, but it's where the provisions of the SYGA were incorporated into existing Florida law.
The Stand Your Ground Act contemplated limited situations under which an aggressor could still use deadly force or force likely to result in great bodily harm, and be justified in doing so. Here's the link to the entire Chapter 776, but concentrate on Florida Statutes 776.041(2).
Even under common law, it's not accurate to say as a generalization that a party who commits assault can never claim self-defense. For example, under a standard application of common law, the assailant can stop the fight, achieve clear physical separation, and state clearly an intent to cease fighting. The assailant still has liability for the initial assault. However, if the other party continues fighting at that point, then the original assailant can practice and claim self-defense from that point forward.
Those elements are incorporated by statute in Florida Statutes 776.041(2)(b) - but allow the use of deadly force without retreat, which often is not permitted at common law without retreat.
If so, this constituted assault with a deadly weapon, and Trayvon would have been fully justified in defending himself with physical force. If he'd had a gun, he would have been justified in shooting his assailant. Since he didn't, he was fully justified in attending himself the best he could.
the assailant can stop the fight, achieve clear physical separation, and state clearly an intent to cease fighting.
Fairly obviously this point is not reached until the victim of assault gets control of the weapon.
I have no idea whatsoever if that is what happened, but it is certainly possible and does not conflict with any of the known facts, AFAIK.