There's a difference between taxing a dollar twice and taxing income twice.

Taxing a dollar twice is the example you used.

Taxing income twice is I invest $10 in a company. the company makes 3% profit for the year, so 30 cents of profit for my investment. Let's say they're taxed on that profit at the end of the year at a rate of 50%. So now of the original 30 cents in profit from my $10 investment, there is 15 cents of profit. When that 15 cents is passed back to the owner (me) it is subject to another round of taxation (10% for this example). So it costs me an additional 1.5 cents just to take control of the already taxed profits i earned. So from the 30 cents of profit, i lose 15 to company taxation, 1.5 to individual taxation, and get left with 13.5 cents of cash in hand. That's one of the reason that structures like REITs are so popular because they allow companies to pass through income to investors without it being taxed at the company level so long as they payout ~90% of earnings.

You can also modify your example to be like the proposed bill. Let's say the person who owns the store is old and doesn't want to run the place anymore. They hire someone to run things and pay them a salary based on how the shop performs, effectively a CEO. If I understand the new bill correctly, the store owner would suddenly not be able to deduct the cost of the CEOs salary when determining the company's taxable income. This means the CEOs salary is effectively taxed at the company level by no longer being deductible from income and then actually taxed at the individual level when the CEO gets it. If the CEOs is actually being paid based on performance though, the increased tax burden will lower the company's profit and thus their own pay which will again be subject to taxes at the individual level. So the CEO's salary is being both taxed directly at an individual level and effectively at the company level where it lowers overall profits.