I am making a simple beef stock from the leftover bones from a New York cut roast beef. Beyond adding a mirepoix and boiling the bones for three hours I'm not doing anything special. When I make stock I typically throw out the leftover meat and vegetables, but do I have to throwout the leftover beef? Aside from the beef I have boiled off the bones I do not have a lot of leftover meat and do not want to potentially waste what could be useable meat.
Taste the meat and if it still seems edible to you then there is no reason to throw it out.
When I make stock, I keep it on a simmer for much longer than three hours and any meat is completely tasteless by the time I'm done. Three hours, however, is about how long you would cook meat to make a stew, so it's quite possible that you could eat it.
On the other hand, not all cuts of meat stew well and I'm not familiar with this cut. If the meat has plenty of connective tissues (i.e. collagen) to gelatinise it shouldn't dry out too much. But the proof is in the pudding: taste it.
I never throw it out. There are plenty of applications for mostly-tasteless meat shreds.
I mostly make chicken stock but I will use the meat shreds in soup, pot pie, casseroles, etc.