Is it true that the burden of proof implies that the person making an allegation should provide evidence of it?

Yes, that is correct. The burden of proof is the responsibility of the person making an allegation to provide evidence to support their claim. In legal proceedings, the burden of proof is typically on the party making the claim or accusation, rather than on the party defending against it. This principle is based on the idea that it is generally easier to prove something than to disprove it, so the person making the claim should be the one to provide evidence to support it.