I'm giving this one to "the Bulls are cheap" crowd for free. Link to Sham's article Have to admit that I took for granted that once the dust settled, they'd sign Teague at 120% of the standard number. However, because they paid Hinrich $3.941M and Belinelli the full bi-annual exception ($1.957M), if they sign Teague to the 120% salary ($1.0284M), they would effectively be hard capped at 13 players. If Teague won't take a lower 1st-year salary, looks like he'll either be traded, asked to play in Europe or renounced. This offseason is really something.
Sham corrected me on this. According to Sham, if they sign Teague to the 120%, they could still sign a rookie FA to a minimum contract ($473,604) plus do two 10-day contracts. However, they definitely could not sign someone like McGrady. Edit: Sham did an addendum article which does a nice job of explaining the Bulls situation and how they got there. Link.