[Batrachian]

"a few nuclei will fuse even in a glass of water from time to time"

Alpha decay is possible due to quantum tunneling, not nuclear fusion at room temperature.

Try this on for size.

[Technogeeb]

Alpha decay is possible due to quantum tunneling,

Yes, that also involves tunneling.

not nuclear fusion at room temperature.

You are mistaken; nuclear fusion does indeed occur at room temperature, just at a very low rate (if you were assuming a zero probability because of the "semiclassical method" in the article to which you linked, bear in mind that it approaches zero only at higher scales, but never actually reaches zero, and is very much non-zero at quantum scales).