counter to indicate hotp count
Your question starts from an assumption that often isn't valid.  You write:


  Assuming the user didn't have to input the OTP value or counter number


but in fact, for cost reasons, often these devices don't haven't any way to send the counter number to the server; the user would have to input it.

If the counter value is actually based upon the time, so it doesn't need to be sent, then yes, the quote from Thomas Pornin doesn't apply.  For those kinds of tokens, yes, the server can use the time and we don't have the issue with it getting desynchronized if you press the button 100 times.  The server does still need to make sure that the token's time approximately matches the server's time, and that the number only increases (to avoid replay attacks).