You're ignoring all costs other than energy, that's all.  The EROEI relates to only a portion of your costs; there is also the cost of all the equipment and the ongoing costs of maintenance and wages.

Consider the obvious example of pumping oil out of the ground.  Sure, there may be even a 2,000% energy return on investment (20 barrels of oil extracted for each barrel of oil equivalent in energy expended) but the overall return on investment will be much lower, perhaps even negative.  Suppose, for example, you spent $10,000,000 to find the oil and to set up all the equipment needed to pump it out.  Great, now you've got yourself a money machine - put $1 worth of energy in and you get $20 out.  But that's not the only cost.  If the machine doesn't work fast enough you may be paying $20 in wages over the time it takes to get that $20 worth of oil out, in which case obviously you're losing money.  Even if your net return on a barrel of oil is positive you may still have a very bad investment, because you just can't pump the oil fast enough to cover the opportunity cost of that $10,000,000.  If that money were borrowed at 5%/year then you need to make $500,000 per year just to cover your borrowing costs.

As for the solar energy payback example - hey, that doesn't make sense to me either!