[natep]

In this case, the "corrections on the fly" refer to all of the real-time responses that the software makes without ground involvement. In the case of a solar limb sensor detecting the sun, the probe will abandon its data collection for that near approach, and go into an emergency response that has been made as straightforward and deterministic as possible, to maximize the chances of recovery for all single-fault and some double-fault scenarios.

To answer your question about software upload, the PSP has 3 redundant CPUs (primary, hot spare, backup spare), and each has multiple boot images. To upload software, the team uploads it to an inactive image of the backup spare CPU, promotes it to hot spare for long enough to collect the data it needs, reboots it into the new image, and then rotates it into the primary role, which is a seamless transition unless something goes wrong, and then the new hot spare takes over again within a second. Once they're sure the software is working, they can update the other CPUs. Before any of this, new software is tested on identical hardware set up on the ground with physics simulations.

See also, "Solar Probe Plus Flight Software - An Overview" from http://flightsoftware.jhuapl.edu/files/_site/workshops/2015/