In looking at the chemistry of 321 stainless, you will notice that it contains titanium as the stabilizing element (i.e. carbon-getter, to prevent the formation of chromium carbides during any sensitization-temperature dwell times). The quantity of titanium addition is in the neighborhood of about five times the quantity of carbon present. In that way, since the formation of titanium carbides is a stronger driver than that for chrome carbides, the titanium will aggressively tie-up as much carbon as possible. This allows the chromium to do what it is supposed to do, namely stay bonded with oxygen so as to form the corrosion-resistant layer of chrome oxide, which makes stainless steel stain less than regular steel.
However, since there is about five times as much titanium present as carbon, when the carbon has been dealt with by the titanium, what happens to all the rest of "free" titanium? If that quantity is significant, the extra titanium may start to bond with any oxygen that it can scavenge, forming titanium oxides on the surface of the stainless, which will resist brazing.
So, depending on the total amount of titanium that is actually present in a given heat of 321 stainless, a brazing shop may or may not find that the titanium creates brazing problems. As a general rule, therefore, I do not ever recommend the general use of 321 stainless for any brazing applications. Instead, I always recommend the use of 304L, 316L or 347 stainless, based on the end-use conditions to be encountered.