How can the Planck length be claimed to be the smallest length?

Many arxiv papers state that the Planck length
is the smallest measureable length.

On the other hand, the gravitational length
L=2Gm/c^2
associated with every electron or proton
is 19 or 22 orders of magnitude smaller
than the Planck length.
Nobody seems to doubt either
of the two statements.

What is the exact answer to this paradox?
One can imagine at least 3 solutions:

1 - Lengths of objects can be smaller than L_Planck,
but not positions.

2 - Lengths can be smaller than L_Planck if
one makes many measurements and then makes
a statistical average.

3 - There is an uncertainty relation between
length L and position x:

L x > L_Planck^2

There might be other answers. What is the
canonical answer by researchers to this question?

Thanks!

John

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