Match play golf?

[ruff-driver]

Pretty sure if an opponent gives you the putt you can't hole out, if you do its loss of hole. Definitely the rule in 4BBB

Nope,
Once given a concession can’t be declined, or withdrawn under any circumstances. So, if you concede a short putt to your opponent, but he putts anyway and misses, it doesn’t matter because he is still considered to have holed out with the putt for the purposes of the match. Rule 2-4.

 

[Hosel Fade]

Pretty sure if an opponent gives you the putt you can't hole out, if you do its loss of hole. Definitely the rule in 4BBB

Not necessarily, the only such thing is if the putt which is conceded could be of assistance to the partner (lets say for arguments sake you have had a bit of the mare and have a 20 footer for double on the same line as your partners 18' for birdie). If you were to putt yours after it were conceded in equity your partner is disqualified from the hole.