Could you clarify with one example:
Consider a merchant who accepts bitcoins. Instead of converting my bitcoings to fiat currency, the merchant is happy to add on to his bitcoins after selling something to me and receiving bitcoins.
Does this transaction require a 10-min confirmation process?
Until confirmed a transaction "could" be double spent. Converting or not converting to fiat makes no difference. How much of a risk the merchant is taking depends on a lot of factors so there is no simple black and white answer. Some factors include the probability of fraud, offline vs online, how much is known about the customer, the ability for the merchant to reverse the sale (steam games for example would suffer essentially no risk/loss by accepting 0-confirm txs*), value of the transaction, and the margin/markup.
As an example soda machines have an average sale of ~$1, have a 70%+ gross margin, and the fraud must be committed in person. On the other hand an online bullion merchant may have an average sale of $1,000+, have gross margins less than 2%, and the attack can be engaged online. A 10-60 minute delay for soda machine is clearly not warranted and wouldn't be viable anyways, on the other hand accepting 0 confirm for bullion is probably stupid and given that shipping is not going to be instantaneous there is really no point to not wait for confirmations.
There is no one answer fits all. IMHO the amount of concern about double spends vastly (by a couple orders of magnitude) the amount of actual double spends.
* On steam games (or other similar company which can revoke access to service). So someone pays for Call of Duty with a double spend. Steam records it as a valid purchase, customers starts downloading, 10-60 minutes later steam's back end is alerted of a double spend in the block. Steam reverses the transaction and user is unable to access downloaded game. Now one could make the argument that user may attempt to break steam's activation (piracy) but there are far easier ways to engage in piracy which don't involve spending any funds (i.e. just illegally torrent Call of Duty). Other companies in similar scenario would be vpn providers, web hosting providers, domain name registrars, online multiplayer games, anything sold as a subscription, and any software as a service (antivirus for example).