Merriam-Webster
www.merriam-webster.com/dictionary/consent
Definition of CONSENT
1 : to give assent or approval : agree
2 archaic : to be in concord in opinion or sentiment
www.merriam-webster.com/dictionary/rape
rapedrap·ing
Definition of RAPE
1 a archaic : to seize and take away by force
b : despoil
Definition of DESPOIL : to strip of belongings, possessions, or value : pillage
Oxford Dictionaries
oxforddictionaries.com/definition/english/consent
noun [mass noun]
permission for something to happen or agreement to do something:no change may be made without the consent of all the partners
verb [no object]
give permission for something to happen:he consented to a search by a detective
oxforddictionaries.com/definition/english/rape
noun [mass noun]
1the crime, typically committed by a man, of forcing another person to have sexual intercourse with the offender against their will:he denied two charges of rape [count noun]:he had committed at least two rapes [as modifier]:a rape victim
archaic the abduction of a woman, especially for the purpose of having sexual intercourse with her:the Rape of the Sabine Women
2the wanton destruction or spoiling of a place:the rape of the countryside
verb [with object]
1(typically of a man) force (another person) to have sexual intercourse with the offender against their will: the woman was raped at knifepoint [no object]:he pleaded not guilty to burglary with intent to rape
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Permission given is exactly that, it is "consent". Rape is by definition "forcing another person to have sexual intercourse with the offender against their will" eg: without consent.
To claim that consent freely given, but not given for reasons other than those which you as an observer deemed to be qualifying reasons, does not make acceptance of that consent an act of rape. Anyone who thinks so is by definition, wrong. There may be other ways to define the issue or scenario which you seek to describe but it most certainly is not rape.