myopenhab.org proxies the full OH REST API. It is and has always been possible to update and command Items through myopenhab.org. If that didn’t work, the UIs themselves wouldn’t work with myopenhab.org.
Anything you can do to OH through the REST API can be done through myopenhab.org. The only difference is having to deal with basic auth. No Items need to be exposed. The exposure of Items is only required for IFTTT integration as that’s how IFTTT gets the events that an Item has changed.
Wolfgang is correct. To see an example using Tasker see Tasker with myopenHAB.org (Screenshots for tasker)