scam email from HP after posting to forum

[Rich9]

I posted a question to the Windows 10 Expert Day forum. 

I didn't get my problem resolved, but I did get a nice email from hp.support.forum@hp.com, telling me that if I didn't get the problem resolved, I could contact HP customer care at [phone number].  The forum won't let me post the phone number.

After talking with HP customer care for a while, without making any progress, and with the technician remoted into my computer, he asked me to pay for some services, and I finally realized that it probably was not really customer care, and I was probably being scammed, so I hung up.  I didn't buy anything, though I'm now worried what malware may be on my computer and what information may be copied off of it.  The email looked legimimate, and all the links were to HP sites.  Presumably the return address was spoofed?  I can post the letter if anybody cares, though evidently I won't be allowed to include the phone number.

I don't know how, but it would be good to warn people that HP doesn't provide a support phone number (at least I can't get to one from the regular customer care number), so if you receive one in response to your forum post, it probably is a scam.

[Rich9]

Further information: I also got an in-forum email from customer_care, who has an account on the forum, with the same message and phone number.  I know not to respond to that, as it comes from a forum user with no posts.  I just needed the warning that email from an HP address isn't really from HP.