Your board supplier is right in questioning the single sided via tent.
If this is a HASL finish, your board supplier can leave the top side open
during Soldercoat and then plug the via hole.  This will solve his
fabrication issue.  What remains is a potential assembly issue, which is
not entirely clear.  There are many existing designs that  utilize all
combinations of via/mask treatments.  I would recommend talking to the
specific assembly house for their input on this design as it relates to
their process.

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