iPhone 4 (ios7) can connect to a hotspot (wifi) but will not see any other wifi networks

I've just inherited an iphone 4 32gb in great condition and am looking to set it up for my son. The phone works perfect on cellular. The phone can connect to a hotspot (wifi) that I set up on my iPad or iPhone 5s. However, the phone can not see any wifi networks. No networks ever show up in the list. At home, at the office, at a hotel... no networks ever show up on the wif list.

The phone is running the latest version of ios7. I have restored the phone via itunes with an operating system refresh.

Still no luck.

Took it to an Apple store to see if I was doing something silly and whether there was just some setting that had gone bad. No luck as the the answer was along the lines of "Yes, sometimes 4 and 4s do that".

I'm confused. If there was a problem with the wifi antenna or chip, shouldn't that prevent the phone from connecting to the hotspots that I set up?

Any advice is much appreciated.

(And apologies if this has been covered before - I've found plenty of "wifi broken after upgrading to ios7" type questions, but none in which the phone retained the ability to connect via hotspot still.)