Is it true that survivors of sexual or domestic violence reporting someone they are/were close to will be interpreted as them consenting to what happened to them?

No.  
Over 50% of all sexual violence is committed by acquaintances, and the team of specially trained Liaison Officers are fully aware of this.  

 
The university’s Sexual Misconduct Policy and the law makes it clear that consent cannot be assumed on the basis of a previous sexual experience or previously given consent, and consent may be withdrawn at any time. The status of someone’s relationship with someone therefore is not important when it comes to sexual misconduct. If consent is not ongoing and the individual does not have the freedom and capacity to consent - then it is sexual misconduct.