The assumptions are different - what contradiction?
The assumptions for the rules on page 127 are different from the assumptions on page 129.
Given that adventurers need to spend much of their time adventuring,
the staff includes a steward who can make payments in the party's
absence (p. 127)
They are adventuring, someone else is running it. As opposed to them managing it directly.
If they hold on to the business, they might feel obliged to spend time
between adventures maintaining the venture and making sure it runs
smoothly. (p. 129)
The roll on the table is to abstract that process, since it is listed in Downtime activities, which is separate from adventuring activities in both the PHB and the DMG. The table is rolled on to see if they succeed or fail, something like an ability check, though this table delves into degrees of success or degrees of failure.
The former (p. 127) assumes a break even status.
An adventurer-owned business can earn enough money to cover its own
The latter (p. 129) allows for either success or failure. Per the Chapter 7 ability check rules, and DMG guidance on ability checks (p. 237):
Only call for a roll if there is a meaningful consequence for failure.
You are better off using the newly acquired inn as an adventure hook.
A raid by local bandits results in the inn burning down
I offer you this as a solution to your perceived problem since D&D 5e sometimes needs a hook for an adventure (your PCs are adventurers primarily) and what better motive could the PCs have for tracking down and defeating / disrupting / neutralizing a group of bandits than that their bar / inn / tavern / investment property just got torched? It's a fine motive.
You can even tie this into a second tier adventure by having the bandits actually be hirelings of a cult leader (a temperance cult) led by a higher CR spell caster, priest, knight, or warlock whose raison d'etre is instituting, in the local region, something like Prohibition. (A ban on drunkenness or drink, what have you).
You now have two small story arcs ready to go for your players.
One, track down the bandits and neutralize them, somehow.
Two: find out who is behind this criminal activity and neutralize
Getting wrapped around the axle on the debits and credits of tavern management isn't what D&D 5e is best at. For that you'll want a different game, called Accountants and Audits.
Well, there isn't really a published game called that, but there should be!
You can do the same thing as above, except rather than bandits torching the Inn/Tavern, the local thieves guild is behind the vandalism since the PCs made a powerful enemy in a previous adventure, unbeknownst to them, and he's trying to hurt them in the pocketbook. They now need to go into investigator mode and figure out who is behind the arson.
Or, take it one step deeper. The inn is built over the ruins of a very old shrine (whose altar stone is hidden under the floor boards of the basement where the ale barrels are stored) where the ritual sacrifice of kender served a deity of law and justice. That religion is experiencing a revival, and the followers hired an arsonist to burn down the defiling building over their holy/unholy ground. The party needs to find out why, and perhaps prevent the rebuilding of a new shrine to that long forgotten deity, demon, or archdevil.
With the above solutions, the contradiction that you perceived is rendered moot. 😊
But which rule should I use?
Whichever one fits what the characters are engaged in: adventuring or downtime.