This is a good point, but I think it applies to most online wallets, correct?
Correct. Which is why blockchain.info is the only web hosted solution that I'm aware of that I'd be willing to call a "wallet".
It certainly applies to any site, like the gambling sites, where you choose to keep a balance or the trading sites like Mt Gox or Bitstamp.
Agreed, which is why you should not store any more at any of those sites than you absolutely must to accomplish your goal. Furthermore, you should be financially, mentally, and emotionally prepared to have the entire balance that you store at any of those sites simply vanish in the blink of an eye. If you feel it would be devastating to lose the amount that you've stored there, then you should have that much there to start with.
Regardless caution is always warranted.
Absolutely
My concern with inputs.io is not so much that the owner isn't trustworthy, he's more walking up to a big imposing building
A big imposing building suggests an investment of several million dollars in establishing a presence. It is very difficult for a building to simply vanish in the blink of an eye. It is also very difficult to purchase a big imposing building without leaving a significant paper trail that would subject you to capture and prosecution if you should fail to deliver on the contracts that you issue.
I just don't see that sort of investment or permanence in a website like inputs.io. A website (like a folding table on the corner) can easily vanish in the blink of an eye and tracing and prosecuting the owner of the site can be extremely difficult.