This is an interesting combination of effects. The chemistry of boron is consistent with becoming tetrahedral, for example boric acid B(OH)4(-) + H(+), BF4(-), BH4(-). That explains why trivalent boron compounds are Lewis acids. In this case, methyl groups are attached which donate electrons and reduce the Lewis acidity of boron.
Di-t-butylether is probably very easy to protonate and therefore generate a tertiary carbocation. Even with a weak Lewis acid, I might think B(CH3)3 would be sufficient to cleave t-butylether.
Could someone confirm the actual experiment results? What did or did not happen? How was the experiment done?