Perhaps I’m not understanding it properly, but sense 1c seems a bit broad to me.
To let come or go in, (1) willingly, as a person does, (2) by physical capacity as a thing. The secondary meanings are earlier in Eng. than the primary, for which native words were in use.
I. As the action of a voluntary agent.
1. To allow to enter, let in, receive (a person or thing).
a place, real or ideal).
b. into any office, position, or relation; spec. in Law, into the possession of a copyhold estate.
c. to do anything.
d. into the number or fellowship of. Obs.
. To allow a matter to enter into any relation to action or thought.
a. To consent to the performance, doing, realization, or existence of; to allow, permit, grant.
b. To allow or receive as valid or lawful; to acknowledge.
c. To accept as true, or as a fact, to concede.
d. With subord. clause. To allow, concede, grant (either from conviction, or for the sake of argument).
¶In these senses admit is sometimes followed by of.
e. admit to (something): to acknowledge (a weakness, etc.); to confess to (doing or being something).
II. As the action of an involuntary agent.
3. trans. To be the channel or means of admission to; to afford entrance, let in. Also absol.
4. To have the capacity to allow to enter, to have room for.
5. To allow of the co-existence or presence of; to lie open to, be capable of, or compatible with.
. or arch
b. with of.