I've never heard of the Rental's song "Friends of P," but in Seattle a "P-Patch," or a "Pea Patch" is a lot set aside by the city for a neighborhood garden.  The program has been around for years (at least since the late '80s).

Does "Friends of P" have anything to do with urban gardens? 

I'm not sure this was a serious query - but I can report that there were P-Patches in Seattle when I was a hippie kid in Seattle in the mid-1970s - probably about the time Matt Sharp was born ;-).  Lots of neighborhoods had these open spaces used for community gardens.  I was told years later that the "P" referred to the Picardo family, farmers that allowed needy families to use their spare land to grow food in the city and these "P Patches" came to be commonplace.  That might be an urban legend.  But the P-patches were a city program by the 1970s, I think.  I live in Texas now, but the P-patches are a great example of why I miss Seattle so much!

Well I'm just amazed that I'm not the only person who still listens to the Rentals. Was Matt Sharp's solo stuff ever any good, I never got around to checking it out?

I disagree.  There is a new one near Greenlake, and it is gorgeous.  By the way, I hope you are semi-kidding about the whole Seattle / density thing.  There are so few P-patches in the city that your plan to build condos on them wouldn't do much.

And as for your description of Seattle as "a big suburb where everyone drives their car solo to get everywhere", I'm not sure what you are talking about.  Seattle may not be as high density as many east coast cities, but if you think Seattle is like a low density suburb, and you think lots of folks drive cars in Seattle, you obviously haven't been to Shoreline, Edmonds, Lynnwood, Bellevue, Kirkland, Redmond, or any of the hundreds of true suburbs that outlie Seattle.

It was a "modest proposal," folks! Sorry if my satirical intent wasn't clear: no, I don't really think converting P-patches to condos would made a whit of difference to Seattle's low-density problem.
However, I do believe that Seattle is a low-density suburb posing as a real city. Whenever I say that, some well-meaning Seattleite inevitably defensively chimes in: "But I bike to work!" Listen, that's called anecdotal evidence, folks, and it just doesn't cut it. Yes, a small percentage of people live like urbanites in real cities like Portland and Vancouver, but you cannot escape the general reality: Seattle is one of the worst American cities in terms single-occupancy vehicles, proportion of single-family homes, and use of public trans. 
But if it's anecdotes you want, here you go. I grew up in NY and lived for 20 years in Chicago. Never owned a car until I moved to Seattle, and now my partner and I are about to become a two-car family -- because it's been simply impossible to find a job within a decent bus ride away from home (development in Seattle having grown up around the car rather than around an urban core with public trans). 
There is an enormous anti-density bias out here -- the first time I heard someone denounce density was when I came here (our real estate agent warned us off of certain neighborhoods because of their density). And my jaw just about dropped when my brother-in-law, a native of these parts, told me that "the problem with Seattle is that the lots are just not big enough." And this is an otherwise good cosmopolitan liberal, yearning for a more suburban lifestyle! Completely unaware of how destructive of the environment that lifestyle is. 
No, Seattle isn't a suburb like Lynnwood (are we being a little too literal, maybe?), but it's generally got a suburban attitude (see my anecdotes above, see the huge resistance to all proposals to increase density) and most of the city has a suburban layout -- single-family homes where most people drive.

Do you deny that Seattle has terrible public trans? Do you deny that the vast majority of Seattleites drive solo in their cars to get to work? Do you deny that most Seattleites live in single family homes (and thus use lots more energy than people living in multi-family structures)? 
None of this is particularly controversial. Do I really have to spend time searching out a link to prove this utterly banal point, a claim that is not even denied by the flat-earthers who want to keep density down. Geez, I just saw a locally produced program on KCTS about transportation planning in Seattle and they went on and on about how behind the times Seattle is in terms of public transportation. I think the number they cited for solo drivers was 78 percent of Seattleites. 
See, the thing about anecdotes is this: if they back up a larger truth, and they are used to illustrate that general point, they are a legitimate rhetorical mode. But use of anecdotes is illegitimate if someone says, "Hey, I'm a resident of Los Angeles, and I take the bus, so Los Angeles must be a fabulous place for public trans!" Or, say, "My grandmother smoked and she lived to 98, so smoking must help you live longer."
You see, the anecdote doesn't align with the general statistics. Whereas my anecdotes do align with the general statistics. 

I couldn't find any report, from KCTS or anywhere else, that "78 percent of Seattleites" were "solo drivers" (presumably to work).  The most I could find was old data from 1996 indicating that 74% of the people in the greater Puget Sound area drove to work in single-occupancy vehicles.  This was a measure of commuters in the entire region, spanning from Tacoma to Everett, not just Seattlites.  Maybe that's what you saw?