Yes, actually a lot like that, because in the mechanical world you'd order from either McMaster-Carr or Grainger. They're largely equivalent in broad strokes, no one would fault you for favoring one over the other.
In 2015 that was the exact same situation for DigiKey and Mouser. Small differences, both have great selection, great service, competitive prices.
This would be like either Grainger or McMaster-Carr just shitting the bed. It would be shocking to hear a consensus of serious mechanical engineers saying "When people order from Grainger, that's a huge red flag for me."
It's also interesting because all four of these companies cater to professionals. And as a professional you never want to be talking to customer service, even if it costs you extra.
I don't think I know how to contact Mouser CS, because I've never had to. And I buy a lot of parts. Enough that we've spent more on overnight shipping this year alone than the article's entire spend. I'm guessing that's related!
But I do know how to find Digi-Key's customer service, and I'm growing increasingly annoyed with them as a company. Not dropping them or anything rash. Just... annoyed. Their continued misadventures with their same-day shipping deadline have cost me a lot of money. So yay! Parties all around!
Mouser customer service (at least 5 years ago) as a big purchaser (University) was excellent. They would do things like screw up an order and then send the replacement free of charge, even for $300 parts. But then the uni order book was probably hundreds of thousands if not millions a year, so it's nothing on their margins.
Grainger has a local rep and that makes a big difference for us. We are always biased towards local support, even when there is a reasonable price differential. It can save your bacon if you have any questions/problems before or after the sale.