"Do people really associate a brands reputation with the content of the site on which they may be advertising?"

Probably. There's overwhelming evidence (in general; not web specific - but I'm not aware of any research which shows it doesn't apply online) which shows advertising context is critical in market positioning.

Have a look at the Tesco-Levi lawsuit from a few years ago, Levi a premium jeans company sued Tesco a supermarket to prevent it selling Levi jeans, because putting premium jeans alongside vegtables damaged the exclusivity of the Levi brand.

While I appreciate the example is from a different context, I believe there's no reason that the same principle don't apply online.

Another way of looking at it - think about the following scenario: Say a consumer was looking at a porn site and it contained an advert for a dating service (called A), and later on the consumer looked at their church's website and it also had an advert for a dating service (called B). If you questioned the consumer about which dating service was more "wholesome" I'm willing to bet the consumer would pick B over A the vast majority of the time.

That's a pretty extreme case and wonderfully framed to back up your assertion, but even it is kinda wrong IMHO.

Dating sites in particular tend to promote the values their clients hold. If it's a dating site where "wholesome" is the clients primary value then advertising on a porn website would be detrimental, however a company like adultfriendfinder benefits greatly from advertising on porn websites.

What I assumed we were talking about was actual big brands like McDonald's or Nike. They, unlike dating sites, tend not to be as dependent on their customers moral values and so context isn't as important.

If you want a big company example look at what Burger King did to McDonalds in the late-70s/early-80s, BK decided to position themself in the adult burger market and move away from the childrens market. BK stopped running adverts during childrens tv.

McD's own adverts carried on running in between kids shows, the context of the ads (in contrast to those of BK) caused McD to seem like a childen's brand. This allowed BK to steal a massive chunk of McD's market share.

McD's own advert harmed the McD brand purely because of context.

While there were clearly other factors at play here, the context in which those adverts ran was a major contributing factor. You could see how the same could apply today with regards to adverts appearing on children's websites, etc.

That's true of traditional TV advertising, though I was under the apparently mistaken idea that internet advertising was what we were discussing.