Not a lawfag but after reviewing the Constitution, Article I Section 2 and 3, and below definition of impeachment from Black's Law Dictionary 2d Addition, it sounds like POTUS is correct in stating that the Senate can set the date for the Impeachment Trail without Speaker Pelosi submitting the Articles. And until the Impeachment Articles have gone to trial in the Senate they are nothing more than an accusation.
>IMPEACHMENT
TheLaw.com Law Dictionary & Black's Law Dictionary 2nd Ed.
(A) const. law, punishments. Under the constitution and laws of the United States, an impeachment may be described to be a written accusation, by the house of representatives of the United States, to the senate of the United States, against an officer. The presentment, written accusation, is called articles of impeachment. 2. The constitution declares that the house of representatives shall have the sole power of impeachment art. 1, s. 2, cl. 5 and that the senate shall have the sole power to try all impeachments. Art. 1, s. 3, cl. 6. 3. The persons liable to impeachment are the president, vice-president, and all civil officers of the United States. Art. 2, s. 4. 4. The offences for which a guilty officer may be impeached are, treason, bribery, and other high crimes and misdemeanors. Art. 2, s. 4. The constitution defines the crime of treason. Art. 3, s. 3. Recourse must be had to the common law for a definition of bribery. Not having particularly mentioned what is to be understood by other high crimes and misdemeanors, resort, it is presumed, must be had to parliamentary practice, and the common law, in order to ascertain what they are. 5. The mode of proceeding, in the institution and trial of impeachments, is as follows: When a person who may be legally impeached has been guilty, or is supposed to have been guilty, of some malversation in office, a resolution is generally brought forward by a member of the house of representatives, either to accuse the party, or for a committee of inquiry. If the committee report adversely to the party accused, they give a statement of the charges, and recommend that he be impeached; when the resolution is adopted by the house, a committee is appointed to impeach the party at the bar of the senate, and to state that the articles of impeachment against him will be exhibited in due time, and made good before the senate, and to demand that the senate take order for the appearance of the party to answer to the impeachment. The house then agree upon the articles of impeachment, and they are presented to the senate by a committee appointed by the house to prosecute the impeachment; the senate then issues process, summoning the party to appear at a given day before them, to answer to the articles. The process is served by the sergeant-at-arms of the senate, and a return is made of it to the senate, under oath. On the return-day of the process, the senate resolves itself into a court of impeachment, and the senators are sworn to do justice, according to the constitution and laws. The person impeached is called to answer, and either appears or does not appear. If he does not appear, his default is recorded, and the senate may proceed ex parte. If he does appear, either by himself or attorney, the parties are required to form an issue, and a time is then assigned for the trial. The proceedings on the trial are conducted substantially as they are upon common judicial trials. If any debates arise among the senators, they are conducted in secret, and the final decision is given by yeas and nays; but no person can be convicted without the concurrence of two-thirds of the members present. Const. art. 1, s. 2, cl. 6. 6. When the president is tried, the chief justice shall preside. The judgment, in cases of impeachment shall not extend further than to removal from office, and disqualification to hold and enjoy any office of honor, trust, or profit under the United States. Proceedings on impeachments under the state constitutions are somewhat similar. Vide Courts of the United States. (B) evidence. An allegation, supported by proof, that a witness who has been examined is unworthy of credit. 2. Every witness is liable to be impeached as to his character for truth; and, if his general character is good, he is presumed, at all times, to be ready to support it.
https://dictionary.thelaw.com/impeachment/
Additionally, Rekieta Law provides some good insights on the only impeachment dispute the Supreme Court has ruled on.