Agreed, with the exception [nitpicking, perhaps] of the technically incorrect second sentence. Intrastate commerce alone can be a sufficient use if such use has a sufficient impact on interstate commerce to constitute use in commerce. In re Silenus Wines, Inc. 194 USPQ 261,267 (CCPA 1977)
"The word “commerce” means all commerce which may lawfully be regulated by Congress. " 15 USC 1127 Of course, the overwhelmingly used basis for date of first use is date of first use in interstate commerce, but in today's Internet based society a website might be viewed internationally even though goods only sold locally, so the term "use in commerce" gets blurred as Congress can and does certainly regulate Internet usage under the Commerce Clause.
The typical situation where intrastate use is sufficient is where an establishment, for example a restaurant, serves interstate customers. See Larry Harmon Pictures Corp. v. Williams Restaurant Corp., 18 USPQ 1292,1295 (Fed Cir. 1991) The reason I mention this is that several of my Illinois trademark clients have primarily Missouri customers since Alton is just across the Mississippi River from the much larger town of St. Louis.