This is not HP. HP does not use 3rd party technical support and a cursory investigation yields that this particular phone number also pretends to be tech support for other vendors like skype and yahoo.
IT Solutions is the company name that they claim to be and are not official. Within the first minute, a request was made to allow them to control my computer remotely. I disconnected the call.
The number I used to reach customer support for HP is 1800 3345144