I see three relevant sentences in the rules.
"The Runner cannot have programs installed that have a combined memory cost greater than his available Memory Units (MU)."
"If the MU costs of the Runner's installed programs ever exceed his available MU, he must trash his installed programs until he is no longer exceeding his availble MU".
"The Runner can choose to trash any number of his installed programs at the beginning of an install program action."
I can see where you're inferring (and it's a fair inference) that you can't install a program if you don't have the memory for it; but I don't see that written in the rules anywhere.
Rules 1 & 2--taken together--would seem to suggest that you can install programs over your memory limit and are just forced to immediately trash down, which would create a simultaneous timing conflict with effects that happen on install and passive effects.
The existence of Rule 3 would seem to suggest that there is a rule that you need to have available memory in order to install a card--because otherwise there'd be no reason to trash programs at the beginning of an install program action (as an aside, this rule limits game space in that they can't make future Corp cards that host on Runner programs because they're basically unplayable without a "host program cannot be trashed" rider; so that suggests that this rule is meaningful). The idea that you can start an install and then have to trash down before the install completes seems like a misreading of this rule.
I was hoping for some clarification on the issue, but I guess I'll just email FFG about it.