Search engine optimization is not the most straight forward marketing tactic that has ever existed...which is the cause of many SEO myths. Let's explore a 5 of these myths.
The "Paid Search has an Effect on SEO Theory"
If these theories were true it would completely destroy the reason people use Google in the first place: relevant search results. Without searchers using Google as their primary search engine their ad revenue would plummet. If you've ever noticed a correlation between who shows up in the paid search and organic search it is not a coincidence. If the same people are in both they are likely online marketing rockstars and understand the importance of a complete online marketing strategy.
Despite Matt Cutts denying this myth, it will continue to exist. You'll hear the same debate about Facebook ads.
I'm Getting a New Website...it Will Already be More SEO Friendly than the Old One
This might be partially true depending on how your old site was done, how old it is, how much content you had etc. Just remember, a new website doesn't mean a new SEO strategy or even a website that was developed to be SEO friendly. Developing and building-out a truly friendly SEO website takes significantly longer, not to mention everything that comes after the build-out. You'll want to be sure that your old URLs are mapped appropriately to your new URLs using a 301 redirects, reporting, monitoring, updating, conversion tracking, etc. If you are going for a budget website, don't plan on it being more SEO friendly just because.
SEO is All About META Tags and Search Engine Submissions
We Did SEO on Our Site Several Years Back...We're Good
Just because you "did SEO" several years back doesn't mean the strategies are relevant today. Many SEO firms out there follow trends on what they think will work, but might be pushing the envelope between white hat and black hat SEO. Search engines are much smarter these days and can find things like that pretty easily, which in turn could negatively impact your traffic and visibility. Even if they aren't unethical practices, it doesn't mean they will work years later. Take for instance guest blogging. A few years ago this was a way to get inbound links to your website while increasing content on someone else's site. As a guest blogger you could control where and how the links to your own website were implemented. Guest blogging is no more and if it was a frequent practice in the past, it may negatively affect you in the future. Here's an article from Matt Cutts on the Death of Guest Blogging for SEO.
This Other Company Guaranteed 1st Page Results
Well if they guaranteed you that I guess it's not a myth. I would however question what they are guaranteeing you first page results for. If they are guaranteeing 1st page results for a term that has no competition or is your brand name then maybe they can do it...but is there value there? With a true SEO strategy, there is no way to guarantee 1st page results...there are just too many factors. Coincidentally the firms promising this are probably the same ones cold calling you. If a firm had this power they wouldn't need to call anyone, they would be busy for years to come.