Ok. What about your database password? I think that your application will always have files that it should read for configuration files or other passwords...
Disclaimer: I'm biased because we run a web service that let's you manage your own servers. But the reason why we created that web service is because of the reasons below:
For our clients and our own projects we've switched to using our own servers/VPS's.
I think PaaS is great for getting simple apps up and running that don't have a lot of external dependencies. However, the PaaS I used (Heroku/EngineYard/AWS) don't perform good enough compared to VPS or servers at "traditional vendors" or things like DigitalOcean.
Also, some of our customers need to have their servers in a geographic location close to home or under national legislation and they don't want to be dependent on a "massive" infrastructure where they can't just pick up the phone and call someone.
Also with local vendors. Problems are usually solved more quickly and communication lines are shorter. You have an answer on a problem much sooner. It also helps that these local vendors do not have massive infrastructures that are hard to fix or hard to move in a short manner of time when something really bad is going on. I have better experience with smaller traditional vendors in fixing problems than I have with "the big guys".
Heroku, for example, is largely dependent on AWS. If AWS fails somewhere, you can't just move somewhere else. Because the deployment procedures and infrastructure is vendor-specific to Heroku. You're kinda locked in. Addons for external services like Redis, Search daemons, logging, etc. is great for ease of use. But if some of those hip startups die, don't get funding or they just have technical/security problems you can't "just move away" because you're pretty locked in.
The above reasons are some main reasons why we moved to 100% of our own servers at local vendors. We have some at DigitalOcean and some at TransIP, which is a Dutch vendor with a long track record and we can by without a credit card with "regular" Dutch payment methods and contracts.
The main problem with "do it yourself" servers/VPSs seem to be the time and effort you need to put in to get everything up and running. PaaS services take care of all this for you. This comes at a price both economically and technically. If you're fine with that price, than I think PaaS is good for you.
If you're not "fine" with that price. You run into the problem of reading through guides, documentation, fiddling with your servers, keeping them updated, managing security, etc. etc. All kinds of problems you need to solve.
Luckily, there is Managed Hosting at some web services and applications that takes care of all this. There's stuff like Plesk, DirectAdmin and such. But they are pretty outdated and not really useful if you're a Rails company.
Luckily, you can use a service that does server/cloud management for you like Commando.io, IntercityUp.com or Cloud66.