What Colin_T said. Yeah!
And also what Kaisa said - all kinds of things, including fish parasites and disease, can be brought in on plants - my usual LFS keeps fish in with their plants, as I believe most do, and I've had anchor worms, ich and other nasties, as well as the detritus worms we usually term planaria and others, come in, the latter even on plants that were bleach dipped (albeit probably too quickly) and soaked in dechlor for hours after rinsing.
When I started quarantining plants, (after dipping,) I still had nasties hatch out, sometimes weeks later.
I've seen people actually announce essentially that poor conditions produce living organisms like magic - no natural laws need apply - so engrained has this assumption become.
Although here I believe Colin_T, in his excellent comment, was merely suggesting remedies for conditions often present in pronounced cases, not stating that these were the cause in every case.
We now get aquarium critters and diseases brought in from round the world...
Of course, the diseases aren't often visible, and may lie dormant until some stressor - which may include unnoticed parasites or other disease having gradual deleterious effect - lowers the immune system of the now-susceptible fish, but diseases - like aquarium pests - aren't spontaneously created out of 'bad conditions' but arrive from somewhere...
And I've had phenomenal hatchouts of multiple critters from internet plant ordering, including white worms, in new tanks or those completely redone (having had none of these while running previously) with entirely new set-ups - substrate, hardscape, plants, with no fish/fish food ever having been in them, or in one case very little for a very short period, as with one guppy in for several days, with two tiny fragments of flake food added - although it may take as long as several weeks for the results of such hatch-outs to manifest.
And in established tanks which have had some of these plants added, I had large quantities of white worms and other critters appear, although the former gradually died down (and again after an outbreak when some unnoticed plant melt sneakily occurred in the back of a tank,) and I haven't noticed any worms at all lately in tanks where great numbers had been evident on the glass, while at least some of the other swimming critters in one evidently feed on live plants at some point in their life-cycle.
Such organisms may propagate according to food source, but this also includes (usually dead) plant matter and mulm under gravel, the last being particularly necessary for plant health and growth in tanks with inert substrates and Walstads - and they may also congregate in filters, I've heard.
These critters, like algae, survive under similar conditions to those in which our fish and plants do, and while they may propagate more rapidly in tanks which are cleaned less often/thoroughly or overfed, the fact of their existance, like that of disease, doesn't necessarily mean that the tanks are neglected or mismanaged in any fashion.
If our tanks were inhospitable to life of that type, it would also be so for our pets.
Darn it.
Tolak - the chances of picking of nasties from fish tanks is apparently greatly reduced by washing thoroughly with soap after (I always promptly wash up to the elbows after each tank, perhaps a rather half-hearted effort where I've been in up to the armpits, although this only occurrs in a couple of tanks in my case) but it also reduces the chance of transmitting any problem from one tank to another.
Personally, I'd flood washing-up gloves every time, trapping bacteria in the gloves against my skin, besides needing a separate pair for each tank, or sterilization between tanks, unless all fish and plants were long-term with nothing lately introduced...
I suppose surgical gloves might answer, at least where cuts/scratches on hands were involved, but you'd be exuding chemicals...
Personally, I'm sticking with the immediate-wash-and-hope-for-the-best method, which generally seems to work well enough, with risk really only enhanced if you have open cuts or scratches - because you still have to care for your fish no matter what.