Former Vice President Mike Pence has confirmed that he took notes on his conversations with former President Trump leading up to the Jan. 6 riot, as Trump repeatedly pressured him to reject the results of the 2020 election during the certification in Congress.
“the broken clock just so happened to coincidentally align with the current time” Kinda exactly what the phrase is used for.
“ A broken clock is right twice a day” is the phrase. 
I know, you were saying the phrase doesn’t apply, but it does.
Stopped clock, if you’re an “eat your cake and have it too” type of person, because a broken clock might be broken in that it runs fast, slow, or be missing teeth on a gear or sometime causing it to skip.