Given time to recover from her own sense of embarrassment and shame, Sam might have been willing to engage in a less charged exchange and explain why she reacted to Helen's tweet in the way she did. A reasonable and calm exchange might well have led to an apology, but on being confronted with a permanent reminder of her mistake and being held up as an example by someone relatively influential, and with a large following of similarly influential people, this became untenable. The fall-out from this has made it a far bigger and nastier episode than was merited.
A little show of maturity at the beginning could have avoided all this unpleasantness. Now direct communication has totally broken down and both sides feel they can't back down. I find this all incredibly sad, not to mention frustrating.