The definition of solo mining is someone who isn't sharing/pooling the "work". Whether or not they run their own node isn't changing that.
no two asics do the same work on any pool.
as thats just inefficient
if you own a cleaning company. and there is 5 different toilets under your management and contract. and you direct the cleaners what to clean..
you dont send all cleaners to clean one toilet. you as a cleaning manager(pool) send one cleaner to each toilet and scrub each toilet until they are all clean
a solo cleaner chooses her own toilets to clean and cleans as many as she can without a manager