By the way, a broken wrist is a major issue for a basketball player. Wrists are very important.
As for turf toe, it is a ligament issue and there are many different grades. There have been football players miss an entire season because their turf toe was really bad. Turf toe is not just about pain tolerance. There is a possibility for it to be re-injured or made worse by playing through it.
From WebMD:
"The basic treatment for treating turf toe, initiailly, is a combination of rest, ice, compression, and elevation (remember the acronym R.I.C.E).This basic treatment approach is to give the injury ample time to heal, which means the foot will need to be rested and the joint protected from further injury. The doctor may recommend an over-the-counter oral medication such as ibuprofen to control pain and reduce inflammation. To rest the toe, the doctor may tape or strap it to the toe next to it to relieve the stress on it. Another way to protect the joint is to immobilize the foot in a cast or special walking boot that keeps it from moving. The doctor may also ask you to use crutches so that no weight is placed on the injured joint. In severe cases, an orthopaedic surgeon may suggest a surgical intervention.
It typically takes two to three weeks for the pain to subside. After the immobilization of the joint ends, some patients require physical therapy in order to re-establish range of motion, strength, and conditioning of the injured toe."
So based on this, he still probably has a week or two until the pain subsides (end of January). Then, he will probably have to rehab the injury to gain strength back. That could take several weeks as well. They are not going to rush him back from this and turf toe is obviously not something you can just play through if your pain tolerance is high enough.