I think there are good reasons to think that there might be little to no profit. High-end phones usually have around a $200 parts cost. Then it costs money to assemble it, transport it from Asia, transport it to a user's doorstep or store, package it, write the drivers for it, test it, design it, license the IP for everything from GSM to ActiveSync and H.264. You need to build in a cushion to handle returns that you then can't sell as new, a cushion to handle warranty repair, a cushion to handle tech support. Heck, Forrester Research estimates that a call to tech support costs them $33. Whether these costs are being paid by Google or LG isn't really important, just that they exist as costs.
It's somewhat hard to see the Nexus 4 doing better than scraping by. Now, Google might be counting on selling these to lower-cost customers via a low-cost chain. Maybe they're direct shipping from Asia and keeping very few on hand and assuming that the techies they sell to will make few tech requests and the only warrantee service they'll need to provide will be when something is actually truly wrong.
I guess it's hard for us to see the profit there. You're right that there's nothing we can cite. Ultimately, it will be interesting to see whether Google keeps this up for many years. Right now, Samsung's GS3 international seems to go for $550. There doesn't seem much compelling about it over the Nexus 4. The HTC One X seems in the same range. Google has been known to underestimate costs like tech support (and simply offer poor support). I think it's possible that Google is underestimating some of the costs here.
Google also is looking to push an agenda. That's wonderful for us as consumers. Anytime a company is looking to push something other than their profits is an opportunity for us to get a good deal - like when a company would rather be popular than profitable. Really, I think what we're really talking about is LG's profit on the Nexus 4 - I don't think it's Google's profit that we're debating, but I have no citation for that either. Google's agenda is to get as many people as possible with smartphones that they can make money off of via search and other things. I wish I could find it, but there was someone from the Android team who had said that Google was trying to prove that a high-end phone could be sold at this price point. The Android team member also noted that people at Motorola disagreed.
Ultimately, here people can have a positive disagreement (one where we disagree because we lack the data that would end the disagreement). Still, the smartphone market has been decently competitive in the Android arena and we've seen many high-end devices being sold nowhere near that price point. In fact, Samsung, HTC, and even LG itself are selling the devices at much higher prices. Heck, T-Mobile is selling the Nexus 4 for more than $500 off-contract. Did LG offer Google a certain number of Nexus 4s on the cheap so Google could prove it's point in exchange for being able to leverage the Nexus brand outside of Google Play at higher prices?
I'd love to think that Google is making a ton of profit on these devices. It would mean that I'd get cool toys much cheaper in the future. Given that Samsung, HTC, and even LG itself can't seem to match that price (or even within $150 of that price), it casts doubt. We'll see over the coming months and maybe Google will be more open. In the meantime, we lack good data and that saddens me because I like data.