Did the AD 30 Jerusalem church accurately represent what the relevantly involved witnesses of Jesus were saying?
The 1st church founded by the apostles in Jerusalem (AD 30) preached on Jesus. What they said about him—his life, ministry, teachings—fit within the general pool of things disciples and general witnesses of Jesus’ life in were saying. So rather than needing to invent Jesus biography and sayings, they simply drew on what the apostles etc. had actually heard and seen. So the 1st church’s preaching did not misrepresent the relevant witnesses. In recounting historical events, they flowed from and with what they perceived to be eyewitness testimony.
In AD 30 Jerusalem, true witness-derived gospel-history was easily accessible, or even hard to avoid, and this includes the facts about whether a purported witness was really saying Jesus appeared to them.
• AD 30-70 Mediterranean, Jesus-bio truths predominated.
• Acts 2 “You all know!” dates to AD 30.
• Jesus-bio witnesses and their testimonies truly flourished in the Jerusalem church.
• In general, ECs were honest about Jesus-bio.
• In AD 30 Jerusalem, witnesses proficiently killed false rumors.
But so what? Plausibly...
• The Jerusalem church wasn't saying Jesus appeared to witnesses
The Jerusalem church strive to reject Jesus-bio not approved (vetted) by involved witnesses.
• In AD 30, 1st church strove to adopt only witnesses' Jesus-bio.
• ECs strove to protect true Jesus-bio.
• 1st church was the nexus of witness knowledge.
But so what? Plausibly...
• The Jerusalem church wasn't saying Jesus appeared to witnesses