In Expressions^x, Before and After^x, Verbs^x

Given the structure: he drew compensation from the team until beginning his investigation in March 2006. One possible paraphrase is as you have written it: he drew compensation from the team until the beginning of his investigation in March 2006. But a better paraphrase is: he...

1) The "has" is required because it shows that it's a present perfect tense, ie. Jones denied using drugs in the past and at present, is still denying it. It's a repetition and continuation of the verb (denied) from the past to the present. If you say "Jones consistently denied", it implies that...