You know, WotC may say that in the rulebooks, but I'm calling BS. Every time I play one of their adventures I sure seem to have zero trouble finding someone to cast Cure Wounds or Lesser Restoration or whatever on my character for a small donation at the local temple.
In Eberron, which was the setting I mentioned, the average priest was an expert with the Religion, and probably Medicine and social skills. In 5e they would basically have the Acolyte background, and as it notes "Performing sacred rites is not the same as channelling divine power."
Clerics generally are marked for far greater things than simply looking after a temple simply by virtue of being Clerics: they go out and do their religion's work.
Or course Eberron does have somewhere that you can go to for healing. In most of the civilised areas there is probably a House Jorasco enclave within a week's travel that can provide low-level magical healing - for a price.
Eberron has a lot of low-end magic, but much fewer high-end magic users around compared to say, Forgotten Realms. That might explain why you had so much access to healing in the adventures. Of course I doubt that anyone would try to claim that FR is a low-magic setting either.
Or your DM couldn't be bothered with the hassle of you having to locate and travel to someone capable of fixing you up, and just wanted to get you back into the plot as soon as possible without the sidetrack.