Does hosting time matter in Search Engine ranking?

Hi all,

I hope this is the right topic to post this under (as this is my first question as Newbie).

I have been offered a free website, but I need to host it somewhere and they pointed me to "a company" (for now I leave it to that).

In the hosting promotional video it was said that "it matters how long your hosting contract with "a company" is in relation to the ranking in Google, Bing, Yahoo, etc.

Their exact words used:
“Remember the longer you sign up for the higher your website will rank in the search engines and the more money you will make.”

That surprised me a bit, as to my (limited) knowledge, these search engines have no clue as to how long I rent space from "a company" to host my site and Google really doesn't care the site will be there tomorrow or not to give it a rank (or am I here totally wrong)?

However it was so consistently promoted that I start to doubt and what place better to ask then here.

So please can the somewhat more experienced people here shine some light on this topic?

I suspect that there might be better deals around the "referring party" does not get commission paid for, but just to be sure I'm not overlooking something simple here.

Thanks