Ceri Subbe said only family had keys to her brother's flat and that he would not have let in a potential killer.
The inquest is expected to examine whether anyone else was involved.
Ms Subbe said her brother had never told her he had been followed or felt threatened.
"I cannot think as to why anybody would want to harm him," she told the inquest.
In a statement read to the court, Ms Subbe said MI6 had been "dragging their feet" over her brother's request to return to government communications surveillance agency GCHQ's headquarters in Gloucestershire.
The mathematics prodigy had worked as a cipher and codes expert for GCHQ since 2001.
End Quote Ceri Subbe Gareth Williams's sisterGareth was like a Swiss clock - very punctual, very efficient, and it was very unlike him not to attend a meeting”
Giving evidence at Westminster Coroner's Court, Ms Subbe added: "The job was not quite what he expected. He encountered more red tape than he was comfortable with."
Mr Williams had asked to return to GCHQ in April 2010 and MI6 had agreed he could leave on 1 September 2010.
The inquest was told that he failed to show up to a meeting that day and Ms Subbe had spoken to one of his colleagues.
"He is very conscientious. The person I spoke to agreed, and said Gareth was like a Swiss clock - very punctual, very efficient, and it was very unlike him not to attend a meeting," she said.
Ms Subbe told the inquest he had seemed upbeat the last time she spoke to him.
She said it was "not particularly" surprising that £20,000 of women's clothes had been found in her brother's flat and that they could possibly have been intended as gifts.
The police officer who discovered the bag in the bath, PC John Gallagher, told the inquest he was let into the locked flat by a letting agent after reports that Mr Williams was missing.
He said that, once inside, his attention was drawn to a woman's wig hanging on the corner of a chair.
When he got to the bathroom, there was a bathrobe on the floor outside the closed door, he added.
When he opened it, he noticed the bag in the bath but only became aware of the "particular smell" of a body when he tried to lift it.
"I noticed that the side nearest the door had a round bulge," he said.
"I noticed there was a padlock with the two zips joined together.
"At this point I am realising it is something serious and my concern was to not damage anything in a crime scene."
He said he could only see red fluid seeping out after he lifted the bag up "by six or seven inches".
He called for back-up and Det Sgt Paul Colgan arrived who cut open the holdall to reveal the body inside.
The inquest has been adjourned until Tuesday.
Opening proceedings earlier, coroner Dr Fiona Wilcox said evidence into Mr Williams's death would be heard in public but that some sensitive information would be withheld because of a "real risk of harm" to national security.
Summaries or "gists" of any withheld evidence would be revealed in court and there would be "a full, fair and fearless inquest into this highly controversial death", she said.
The inquest will hear from Mr Williams's colleagues from MI6 and the GCHQ, toxicology experts and bag experts.
Most of the 37 witnesses will give evidence in person, but some officers will be able to testify anonymously and behind screens.
Broadcasters and newspaper have applied for photographs, video and documents referred to in open court to be supplied to the media.
But a lawyer for the Met Police, Vincent Williams, said there was a "live complex ongoing investigation" into the death and charges were still a "real possibility".
Dr Wilcox suggested that the lawyers agree a compromise outside court.
A lawyer for Mr Williams's family said they opposed the release of video footage showing an attempted reconstruction of how he may have climbed into the bath.
A post-mortem examination and further toxicology tests - which found no trace of drugs, alcohol or poison - and the police investigation have all failed to establish a cause of death.
Police originally found it would have been impossible for Mr Williams to have locked himself inside the holdall his naked body was found in.
But they have been unable to establish whether he died at the hands of a third party.
Dr Wilcox told a pre-inquest hearing in March that whether the code-breaker was able to lock himself in the bag would be "at the very heart" of the inquest.
Lawyer Anthony O'Toole told the pre-inquest hearing that Mr Williams's family believed a third party was present at his death or later destroyed evidence.
"The impression of the family is that the unknown third party was a member of some agency specialising in the dark arts of the secret services - or evidence has been removed post-mortem by experts in the dark arts," he said.