Why people ask it
Because the telephone-game picture is intuitive, memorable, and almost universally repeated.
Short answer
The text can be reconstructed with high confidence from a large, geographically dispersed manuscript record. That answers transmission — whether the content is true is a separate question worth keeping separate.
Deeper answer
We have no originals, which is true of essentially all ancient literature. The relevant question is whether what the authors wrote can be recovered, and that depends on how many copies survive and how independent they are.
Manuscript transmission is a branching public process, not a private linear chain. Copies spread across regions and languages while earlier copies remained in circulation. A corruption in one branch shows up as a divergence from the others rather than becoming the new standard. That is the opposite of telephone.
The variants are real and they are catalogued. Most are spelling and word order; more copies mechanically means more variants. The meaningful ones are printed in the footnotes of any modern Bible — which is what transparency looks like, not what concealment looks like.
Common mistake
Citing manuscript counts as though they establish truth. They establish transmission. Say which question you are answering.
Conversation-ready response
""Textual reliability and theological truth are two different questions. Which one are we actually talking about? I have answers for both, but they are different answers.""
Source notes coming soon.