There are some truths and some half-truths here, and obviously some misunderstandings.
people claim that if you save 75% of your income into tax deferred
retirement accounts, you wind up paying no income tax even with an
income like $100k, since you would only have $25k of taxable income.
Well, that's nice, but what are you going to live on? $25K/year is not much, and a person earning $100K will probably not be able to eat in a soup kitchen and ride old bicycles everywhere while living under the bridge.
I thought the max you could put in a 401k is $17.5k, and the max in an
IRA is $5.5k, meaning you could save $23k. What would you put the
other $50k in?
That's the part of misunderstandings. You cannot save 75% of your income in a tax deferred account if you earn $100K. Maximum allowed per law for employees is about $51K (i.e.: 50%), + 5.5K you can put into an IRA. So we're at about 57%, not 75%.
The 51K are comprised of both the employee contribution (which is limited to 17.5K, as you have correctly pointed out) and the employer's match. Now go find me an employer to match 200%. Never heard of that (except people working for themselves, of course).
Now when people are working for themselves, there's another limit: 25% of the net income (or the compensation, if solo 401(k), in addition to the $17.5K). So if you earn 100K as self-employed - you can only put the same $50K in a tax-deferred account.
So I cannot see how you can save into a retirement account 74K a year.
Also, these same people claim that if you save this much, you could be
financially independent in as little as 10 years
IF you save that much, may be (do the math yourself). But as we've seen, that's a big if.
Do they account for the taxes and 10% penalty for early withdrawl
No, they rely on IRC Sec 72(t)(2)(A)(iv) which allows for periodic payments from the plan to be penalty free under certain conditions.
Bottom line - don't believe them. While there's some grain of truth there, what you described is an exaggeration and misrepresentation of the current state of affairs in this area.