Yep, and you found the cause already. :)
In External HTTP Access it says that none of the external HTTP access transports are available (cURL, Streams, fsockopen).
Which, shortly speaking, means that you can't make external HTTP requests using WordPress HTTP API.
What you could do is ask your hosting provider to allow such capability. Turning it off does not really increase any security and turning it on does not make it insecure either if configured properly.
Another option would be to change hosting provider - there are plenty of them who will provide not such restricted hosting options.
I will add transport capabilities' check to the general plugin health check upon activation - to avoid such situations.
In upcoming versions I might add [client-side] JS based stream status, but not sure as of this moment - it's not as reliable as on server side.
Sorry for inconvenience,