Thus far, to a man, every responder is correct. An ATC clearance directing you to intercept the localizer is not in any way, shape, or form, an altitude clearance. It's a lateral navigation clearance. You've been given a clearance to intercept the localizer and track it inbound (or outbound, as your clearance might be under any given circumstance) as a form of navigation. You have not been given any clearance that ammends of alters your last altitude assignment.
Think of any typical arrival. You may be cleared via XXX arrival, but that is not a clearance to fly the published altitudes. You are cleared for lateral navigation only...you must disregard the published altitudes unless told to "descend via XXX arrival. The same applies when told to intercept the localizer. You have not yet been given any clearance that ammends your last altitude assignment. Until you receive such a clearance, you may not descend, ascend, or even a little of both.
§ 91.123 Compliance with ATC clearances and instructions.
(a) When an ATC clearance has been obtained, no pilot in command may deviate from that clearance unless an amended clearance is obtained, an emergency exists, or the deviation is in response to a traffic alert and collision avoidance system resolution advisory. However, except in Class A airspace, a pilot may cancel an IFR flight plan if the operation is being conducted in VFR weather conditions. When a pilot is uncertain of an ATC clearance, that pilot shall immediately request clarification from ATC.
If you're not certain, obtaining clarification from ATC isn't just a good idea; it's a legal requirement on your part.
If you're acting as PIC and this compadre is your SIC, don't let him cow you down...it's your show; do it properly. If you're flying as SIC and this compadre is really the PIC, and insists of such flagrant violations of basic airmanship, then you need to have a discussion with your chief pilot regarding the matter. You also need to refuse to fly with this individual until he or she is properly educated.
From FAA H-8083-15, Instrument Flying Handbook, Chapter 10:
Once you know which approach you will execute, you should plan for the descent prior to the initial approach fix (IAF) or transition route depicted on the IAP. When flying the transition route, maintain the last assigned altitude until you hear “cleared for the approach” and have intercepted a segment of the approach. You may “request lower” to bring your transition route closer to the required altitude for the initial approach altitude. When ATC uses the phrase, “at pilot’s discretion” in the altitude information of a clearance, you have the option to start a descent at any rate, and you may level off temporarily at any intermediate altitude. However, once you have vacated an altitude, you may not return to that altitude. When ATC has not used the term “at pilot’s discretion” nor imposed any descent restrictions, you should initiate descent promptly upon acknowledgment of the clearance.
From FAA H-8261-1, Instrument Proceedures Handbook, Chapter 4:
It is in circumstances like this that you may be tempted to use the minimum safe altitude (MSA) shown in the planview, although the MSA is for emergency use only, and is not an operational altitude unless you are specifically cleared to that altitude. The ILS procedure relies heavily on the controller's recognition of the restriction upon you to maintain your last assigned altitude until "established" on a published segment of the approach. To be "established" means to be stable or fixed on a route, route segment, altitude, heading, etc. The International Civil Aviation Organization (ICAO) definition of established is considered as being within half full scale deflection for the ILS and VOR, or within ±5° of the required bearing for the nondirectional radio beacon (NDB). Generally, the controller assigns an altitude compatible with glide slope intercept prior to being cleared for the approach.
From the same source and chapter, we read the following; note that being able to descend is predicated on being cleared for the approach (intercepting the localizer is NOT an approach clearance), and upon being established on a published route segment...both must apply. If you establish yourself on a published route segment, you may not vacate your last assigned altitude until cleared to do so. For the purposes of descending on an approach, you
must be cleared for the approach, or specifically cleared to descend in accordance with the approach:
Remember during arrivals, when cleared for an instrument approach, maintain the last assigned altitude until you are established on a published segment of the approach. If you are already on a published segment, you can descend to its minimum altitude.
Again from the same reference and chapter, we read the following:
Upon your arrival in the terminal area, ATC either clears you to a specific altitude, or they give you a descend via clearance that instructs you to follow the altitudes published on the STAR. You are not authorized to leave your last assigned altitude unless specifically cleared to do so. If ATC amends the altitude or route to one that is different from the published procedure, the rest of the charted descent procedure is canceled. ATC will assign you any further route, altitude, or airspeed clearances, as necessary.
From the same source, in the appendix glossary:
Descend Via – A descend via clearance instructs you to follow the altitudes published on a STAR. You are not authorized to leave your last assigned altitude unless specifically cleared to do so. If ATC amends the altitude or route to one that is different from the published procedure, the rest of the charted descent procedure is canceled. ATC will assign you any further route, altitude, or airspeed clearances, as necessary.