This story is probably just strangely pitched, but the idea is that the US Navy has low visibility so it is harkening back to the glory days of the War of 1812. There is so much wrong here.
First, the survey that seems to be driving the story, which has the Army and then the Marines as the services most important for National Defense, seems to have asked people who are ignorant of geography. Just as I often ponder about whether Canada needs an army given its position, clearly the US, for national security, relies far more on its Air Force and Navy. The Army and Marines are not poised to deal with invasions from Mexico or Canada (although Red Dawn suggest otherwise).
But it is clear that the wars in Iraq and Afghanistan have highlighted the ground-folks at the expense of the pilots and sailors. Libya may have helped the USAF get a bit of its mojo back after drones have been taking all of the credit as of late. But the Navy is just doing the usual Navy thing--keeping sea lanes open, dealing with pirates, the occasional terrorist (SEALs are Navy folks--the name should be enough to remind us of that), carriers have been showing the flag and then some, and so on. More importantly for the Navy, it does not have much to fear from budget cuts--whether we need 11 carriers, we are going to keep on having 11 carriers.
Second, most Americans do not remember what they were taught in school about the War of 1812. Are there any good movies covering that war? If not, well, ooops. Why not focus on the war of 1941-1945? World War II was mighty good (except for the first six months) for Navy PR. We are in the 70th anniversary of some major battles: Guadalcanal, Midway, and, oh yeah, Mid-freaking-way!!! That one battle has far more importance, turning the tide in the Pacific; has a big movie with Charlton Heston and an all-star cast; and it has only the Navy. No messy army or army air force roles played by Doolittle or what not.
Third, those folks who do remember the War of 1812 almost certainly do not remember the US Navy playing a big role. Instead, they remember the Battle of New Orleans and Andrew Jackson or the burning of Washington. Yes, Francis Scott Key wrote what became the National Anthem from a ship, but the song is what gets the attention not what Key was standing on at the time.
While it makes sense that Canada plays up the War of 1812 since that pretty much ended the American threat to its existence and solidified their identity, I am pretty sure the US Navy could and should focus elsewhere for examples of excellence and identity.