The problem with HP’s US technical support is typically caused by the “national” HP 2-in-1 Resellers that only ship a box and don’t train the end user and give little to no support after the sale. This fills HP’s call queue up with calls for basic support questions and causes delays in replies.
With HP Latex equipment, there is no reason to purchase from these national resellers. The price on the hardware is the same from every dealer. Companies need to start looking for more local support, specifically a HP 3-in-1 reseller who are also service trained. We know the machines better than the 2-in-1 resellers and typically offer quicker resolutions to any issues that may occur.
As for the OP’s original question, Yes Print Head 01 means head 1 in the carriage. The number will update to show the stall that has a bad head in it. Most of these errors are caused by a print head that has failed electrically. This could be from internal or external damage, so you might not see any issues with the head on visual inspections. If the error happens to a print head that has more than one stall in the carriage you can try to swap the heads and see if the error follows the print head. If it does follow the head then the print head is bad, if it doesn’t then there could be something wrong with the contacts on the carriage or the printer needs servicing. If, like in this case, there is only one stall for that head, you would have to put a brand-new head in to see if it works.