You're acting as if your interpretation is the only valid one. Since not everyone will interpret "the jab stops the spread" as "the pandemic is over", the best we can do is interpret "the jab stops the spread" as ... wait for it ... "the jab stops the spread".

My interpretation would be closer to "the jab slows the spread".

Yeah, to be fair that is probably a more accurate statement.

Edit: and while we're here, here is politifact's take:

https://www.politifact.com/factchecks/2021/oct/14/joe-biden/...

Concluding it's "half true" fits this thread well :)