What's the lowdown on runflats (specifically on Siennas)?

About a year ago I purchased a 2005 Sienna. It wasn't long before I began to experience tire pressure issues. Now I deal with slow leaks in a few. One has been fixed, but here is the real issue:

Apparently, from what I've been reading, my Sienna may have orginally come from the dealer with run flats that have since been replaced with standard tires. I'm now running Grand Tour 215/65r16's all around. These tires were practically brand new when I bought the van and the tread still has a lot of meat. I've already repaired one (did a full remount), another has what I'm pretty sure is a leaky valve stem, but all three of the others leak very slowly over time, probably leaky bead seals.

I decided to check on prices around the area to have all four tires remounted and filled with nitrogen.

I hit a snag with the very first enquirey. The first shop I contacted claims that if the tires are not run flats, my only option (due to what they said are liability issues), was to buy four new tires, all run flats.

So far, from everything I've been reading, what I've been told by these guys is a bunch of whooey. What say you all?

EDIT: I forgot to mention one other thing:

When I first started checking tire pressures I found all four tires had been filled to 45 lbs. until just recently I've kept them all at 45. While in for some accident repair, I asked the shop to check the tires (different shop from the above). They said that they had let ten pounds out of three, and filled the other to 35 based on the door sticker. I'm just now realizing the reason they may have been at 45 is because they aren't run flats and have softer sidewalls. I know it handles incredibly well at 45. 35 is okay, but if I'm right about the sidewall difference maybe they should be harder? Any insight into that situation would be appreciated as well.